The document describes using a decision tree to analyze a company's decision about whether to test market a new product, M997. The decision tree models the possible outcomes and probabilities at each decision point. It determines that the expected monetary value of testing the market is £39.2K, so the company should test market M997. Sensitivity analysis shows the recommendation is robust to changes in some probabilities and payoffs.
The Robust Optimization of Non-Linear Requirements Modelsgregoryg
The document discusses robust optimization of non-linear requirements models. It introduces the defect detection and prevention (DDP) model used at NASA JPL to represent requirements, risks, mitigations, and their relationships. It then describes two algorithms, KEYS and KEYS2, for efficiently exploring the search space of the DDP model to find high-quality, robust solutions. Finally, it benchmarks these algorithms against other search-based approaches like simulated annealing, MaxWalkSat, and A* search.
Outline for Lecture 15Long-Run Production CostsThe Lon.docxgerardkortney
Outline for Lecture 15
Long-Run Production Costs
The Long-Run Cost Curve (five plant sizes)
Suppose that a firm can operate in five alternative plants in the short run, Plants 1 through 5, with respective short-run average total cost curves (ATC1 through ATC5) illustrated by Figure 9.7.
In this illustration, vertical white lines show levels of output at which firm should change its plant to achieve the lowest average total cost.
To see why, suppose that firm produces an output of less than 20 units, say 15 units. In this case, lowest average total cost is achieved in Plant 1 because ATC1 lies below all other ATC curves for 15 units. Provided that plant is a variable resource in the long run, firm chooses Plant 1, indicating that blue section of ATC1 is part of firm’s long-run average total cost curve for output levels below 20 units.
Now, suppose firm raises production to somewhere between 20 and 30 units, say 25 units. In this second case, lowest average total cost is achieved in Plant ____ because ____ lies below all other ATC curves for 25 units. Provided that plant is a variable resource in the long run, firm chooses Plant ____, indicating that blue section of ____ is part of firm’s long-run average total cost curve for output levels between 20 and 30 units.
Similarly, blue section of ____ is part of long-run average total cost curve for output levels between 30 and 50 units, blue section of ____ is part of long-run average total cost curve for output levels between 50 and 60 units, and blue section of ____ is part of long-run average total cost curve for output levels above 60 units.
Given these five cases illustrated by Figure 9.7, how do we obtain long-run average total cost curve? Is it smooth or bumpy? Explain.
The Long-Run Cost Curve (unlimited plant sizes)
The blue long-run average total cost curve in Figure 9.7 is drawn under the assumption that firm can operate in five alternative plants in the short run. However, in modern manufacturing industries (i.e. automobiles, pharmaceuticals, etc.) the number of possible plant sizes is many more than five.
In line with this reasoning, each red average total cost curve in Figure 9.8 represents a possible plant size in the short run.
Given all these red curves illustrated by Figure 9.8, how do we obtain long-run average total cost curve? Is it smooth or bumpy? Explain.
Economies and Diseconomies of Scale
Shape of long-run average total cost curve (Figures 9.8 and 9.9) is explained via economies and diseconomies of scale.
Economies of Scale
In the upper panel of Figure 9.9, economies of scale corresponds to ____ part of the curve; in the output range between zero and q1, average total cost ____ as production rises in the long run.
Explain economies of scale: why is average total cost decreasing with rising output?
Diseconomies of Scale
In the upper panel of Figure 9.9, diseconomies of scale explains ____ part of the curve; in the output range above than q2, avera.
Here are the steps to solve this example:
1. Estimate the total cost function:
TC = a + bQ + cQ^2
2. Take the first derivative of the total cost function to get the average cost function:
AC = b + 2cQ
3. Take the first derivative of the average cost function and set equal to 0 to minimize AC:
b + 2cQ = 0
Q = -b/2c
4. Plug back into the average cost function to get the minimum AC.
5. Compare minimum AC to market price to determine if production should continue.
In this example, the estimated total cost function is:
TC = 700
Decision analysis- OR- Dr. Mohamed Sameh .pdfDinaSaad22
This document discusses decision analysis and its applications. It provides examples of how decision analysis can help companies make complex decisions under uncertainty. Specifically, it details how Phillips Petroleum used decision analysis software to successfully evaluate exploration projects and maximize profits. It then presents a case study of a textile company deciding whether to renew a factory or sell it. Different decision making techniques without and with experimentation are applied, including decision trees, to determine the optimal policy.
This document provides an overview of key concepts in cost revenue analysis, including the production process, fixed and variable inputs, short-run versus long-run costs, the production function, marginal product, the law of diminishing returns, economic versus accounting costs, cost curves, revenue analysis, break-even and shutdown points, and scales of production in the long run. It defines important terms and concepts and provides examples to illustrate them.
EGT267 Programming for Engineering Applications Spring 2020 .docxgidmanmary
EGT267 Programming for Engineering Applications Spring 2020
1
EGT 267 HW-1 (Due on February 20 in the class)
PROGRAMMIING ENGINEERING PROBLEMS
Problem 1: (Conversions) This problem involves converting a value in one unit to a value in
another unit. The program should prompt the user for a value in the specified units and then print
the converted value, along with the new units.
(1) Write a program to convert pounds to kilograms. (Recall that 1 kg = 2.205 lb). The pound
value you input/test is 159 lb.
Problem 2: (Areas and Volumes) This problem involves computing an area or a volume using
input from the user. The program should include a prompt to the user to enter the variables needed.
(1) Write a program to compute the area of a triangle with base b and height h. (Recall that
Aerea = ½* (b * h). ) The b and h values are 1.8 and 6.7 meters, respectively.
Problem 3: (Wind Tunnels) A wind tunnel is a test chamber built to generate different wind
speeds, or Mach numbers (which is the wind speed divided by the speed of sound). Accurate scale
models of aircraft can be mounted on force-measuring supports in the test chamber, and then
measurements of the forces on the model can be made at many different wind speeds and angles.
At the end of an extended wind tunnel test, many sets of data have been collected and can be used
to determine the coefficient of lift, drag, and other aerodynamic performance characteristics of the
new aircraft at its various operational speeds and positions. Data collected from a wind tunnel test
are listed in the following table:
EGT267 Programming for Engineering Applications Spring 2020
2
Assume that we would like to use linear interpolation to determine the coefficient of lift for
additional flight-path angles that are between -4 degrees and 21 degrees (Let’s estimate the
coefficient of lift @ 9 flight-path angle degrees). Write a program that allows the user to enter the
data for two points and a flight-path angle between those points. The program should then compute
the corresponding coefficient of lift.
Homework requirements:
please take two screenshots (one screen shot is for your code; the other is for the results), copy &
past them into your homework, and then submit a hard copy.
Sheet1MAC 7200, CASE STUDY WEEK 61) BREAK EVEN POINTA) IN UNITSSales Revenue16.00 Variable Materials3.00 Variable Labor1.00 Variable Overhead3.50 Variable Marketing Costs1.50Total Variable Costs:9.00CONTRIBUTION MARGIN PER UNIT7.0044%Fixed overhead4.00Fixed Marketing costs2.00Total Fixed Costs6.00BREAK EVEN POINT IN UNITS = FIXED COSTS / CONTRIBUTION MARGIN PER UNITEQUATION16N - 9N - 90,000 = 0Fixed Costs:90,000.007N = 90000CONTRIBUTION MARGIN PER UNIT7.00BREAK EVEN POINT IN UNITS12,857N=B) BREAK EVEN IN DOLLARSUNITS BREAKEVEN12,857SALES PRICES$ 16.00BREAK EVEN IN DOLLARS$ 205,712.00Combined2. SPECIAL ORDER ANALYSISremainder of ca ...
Farmers can produce crops using different combinations of capital and labor. In the US, crops are typically grown using capital-intensive technology, while in developing countries crops are grown using more labor-intensive production. Isoquants can show the different options for crop production using different amounts of capital and labor.
The reference of this book is from Dominick Salvatore's Managerial Economics. It is in chapter 8 with the following topic: Linear Programming, Production process, Feasible region, Optimal solution, Objective function, Inequality constraints, Nonnegativity constraints, Decision variables, Binding constraints, Slack variable, Simplex method, Primal problem, Dual problem, Shadow price, Duality theorem and Logistic management.
The Robust Optimization of Non-Linear Requirements Modelsgregoryg
The document discusses robust optimization of non-linear requirements models. It introduces the defect detection and prevention (DDP) model used at NASA JPL to represent requirements, risks, mitigations, and their relationships. It then describes two algorithms, KEYS and KEYS2, for efficiently exploring the search space of the DDP model to find high-quality, robust solutions. Finally, it benchmarks these algorithms against other search-based approaches like simulated annealing, MaxWalkSat, and A* search.
Outline for Lecture 15Long-Run Production CostsThe Lon.docxgerardkortney
Outline for Lecture 15
Long-Run Production Costs
The Long-Run Cost Curve (five plant sizes)
Suppose that a firm can operate in five alternative plants in the short run, Plants 1 through 5, with respective short-run average total cost curves (ATC1 through ATC5) illustrated by Figure 9.7.
In this illustration, vertical white lines show levels of output at which firm should change its plant to achieve the lowest average total cost.
To see why, suppose that firm produces an output of less than 20 units, say 15 units. In this case, lowest average total cost is achieved in Plant 1 because ATC1 lies below all other ATC curves for 15 units. Provided that plant is a variable resource in the long run, firm chooses Plant 1, indicating that blue section of ATC1 is part of firm’s long-run average total cost curve for output levels below 20 units.
Now, suppose firm raises production to somewhere between 20 and 30 units, say 25 units. In this second case, lowest average total cost is achieved in Plant ____ because ____ lies below all other ATC curves for 25 units. Provided that plant is a variable resource in the long run, firm chooses Plant ____, indicating that blue section of ____ is part of firm’s long-run average total cost curve for output levels between 20 and 30 units.
Similarly, blue section of ____ is part of long-run average total cost curve for output levels between 30 and 50 units, blue section of ____ is part of long-run average total cost curve for output levels between 50 and 60 units, and blue section of ____ is part of long-run average total cost curve for output levels above 60 units.
Given these five cases illustrated by Figure 9.7, how do we obtain long-run average total cost curve? Is it smooth or bumpy? Explain.
The Long-Run Cost Curve (unlimited plant sizes)
The blue long-run average total cost curve in Figure 9.7 is drawn under the assumption that firm can operate in five alternative plants in the short run. However, in modern manufacturing industries (i.e. automobiles, pharmaceuticals, etc.) the number of possible plant sizes is many more than five.
In line with this reasoning, each red average total cost curve in Figure 9.8 represents a possible plant size in the short run.
Given all these red curves illustrated by Figure 9.8, how do we obtain long-run average total cost curve? Is it smooth or bumpy? Explain.
Economies and Diseconomies of Scale
Shape of long-run average total cost curve (Figures 9.8 and 9.9) is explained via economies and diseconomies of scale.
Economies of Scale
In the upper panel of Figure 9.9, economies of scale corresponds to ____ part of the curve; in the output range between zero and q1, average total cost ____ as production rises in the long run.
Explain economies of scale: why is average total cost decreasing with rising output?
Diseconomies of Scale
In the upper panel of Figure 9.9, diseconomies of scale explains ____ part of the curve; in the output range above than q2, avera.
Here are the steps to solve this example:
1. Estimate the total cost function:
TC = a + bQ + cQ^2
2. Take the first derivative of the total cost function to get the average cost function:
AC = b + 2cQ
3. Take the first derivative of the average cost function and set equal to 0 to minimize AC:
b + 2cQ = 0
Q = -b/2c
4. Plug back into the average cost function to get the minimum AC.
5. Compare minimum AC to market price to determine if production should continue.
In this example, the estimated total cost function is:
TC = 700
Decision analysis- OR- Dr. Mohamed Sameh .pdfDinaSaad22
This document discusses decision analysis and its applications. It provides examples of how decision analysis can help companies make complex decisions under uncertainty. Specifically, it details how Phillips Petroleum used decision analysis software to successfully evaluate exploration projects and maximize profits. It then presents a case study of a textile company deciding whether to renew a factory or sell it. Different decision making techniques without and with experimentation are applied, including decision trees, to determine the optimal policy.
This document provides an overview of key concepts in cost revenue analysis, including the production process, fixed and variable inputs, short-run versus long-run costs, the production function, marginal product, the law of diminishing returns, economic versus accounting costs, cost curves, revenue analysis, break-even and shutdown points, and scales of production in the long run. It defines important terms and concepts and provides examples to illustrate them.
EGT267 Programming for Engineering Applications Spring 2020 .docxgidmanmary
EGT267 Programming for Engineering Applications Spring 2020
1
EGT 267 HW-1 (Due on February 20 in the class)
PROGRAMMIING ENGINEERING PROBLEMS
Problem 1: (Conversions) This problem involves converting a value in one unit to a value in
another unit. The program should prompt the user for a value in the specified units and then print
the converted value, along with the new units.
(1) Write a program to convert pounds to kilograms. (Recall that 1 kg = 2.205 lb). The pound
value you input/test is 159 lb.
Problem 2: (Areas and Volumes) This problem involves computing an area or a volume using
input from the user. The program should include a prompt to the user to enter the variables needed.
(1) Write a program to compute the area of a triangle with base b and height h. (Recall that
Aerea = ½* (b * h). ) The b and h values are 1.8 and 6.7 meters, respectively.
Problem 3: (Wind Tunnels) A wind tunnel is a test chamber built to generate different wind
speeds, or Mach numbers (which is the wind speed divided by the speed of sound). Accurate scale
models of aircraft can be mounted on force-measuring supports in the test chamber, and then
measurements of the forces on the model can be made at many different wind speeds and angles.
At the end of an extended wind tunnel test, many sets of data have been collected and can be used
to determine the coefficient of lift, drag, and other aerodynamic performance characteristics of the
new aircraft at its various operational speeds and positions. Data collected from a wind tunnel test
are listed in the following table:
EGT267 Programming for Engineering Applications Spring 2020
2
Assume that we would like to use linear interpolation to determine the coefficient of lift for
additional flight-path angles that are between -4 degrees and 21 degrees (Let’s estimate the
coefficient of lift @ 9 flight-path angle degrees). Write a program that allows the user to enter the
data for two points and a flight-path angle between those points. The program should then compute
the corresponding coefficient of lift.
Homework requirements:
please take two screenshots (one screen shot is for your code; the other is for the results), copy &
past them into your homework, and then submit a hard copy.
Sheet1MAC 7200, CASE STUDY WEEK 61) BREAK EVEN POINTA) IN UNITSSales Revenue16.00 Variable Materials3.00 Variable Labor1.00 Variable Overhead3.50 Variable Marketing Costs1.50Total Variable Costs:9.00CONTRIBUTION MARGIN PER UNIT7.0044%Fixed overhead4.00Fixed Marketing costs2.00Total Fixed Costs6.00BREAK EVEN POINT IN UNITS = FIXED COSTS / CONTRIBUTION MARGIN PER UNITEQUATION16N - 9N - 90,000 = 0Fixed Costs:90,000.007N = 90000CONTRIBUTION MARGIN PER UNIT7.00BREAK EVEN POINT IN UNITS12,857N=B) BREAK EVEN IN DOLLARSUNITS BREAKEVEN12,857SALES PRICES$ 16.00BREAK EVEN IN DOLLARS$ 205,712.00Combined2. SPECIAL ORDER ANALYSISremainder of ca ...
Farmers can produce crops using different combinations of capital and labor. In the US, crops are typically grown using capital-intensive technology, while in developing countries crops are grown using more labor-intensive production. Isoquants can show the different options for crop production using different amounts of capital and labor.
The reference of this book is from Dominick Salvatore's Managerial Economics. It is in chapter 8 with the following topic: Linear Programming, Production process, Feasible region, Optimal solution, Objective function, Inequality constraints, Nonnegativity constraints, Decision variables, Binding constraints, Slack variable, Simplex method, Primal problem, Dual problem, Shadow price, Duality theorem and Logistic management.
The document discusses four market structures: pure competition, pure monopoly, monopolistic competition, and oligopoly. It provides details on the characteristics, pricing, and profit maximization analysis of perfect competition and pure monopoly. An example is given to illustrate the cost structure and profit calculation of a perfectly competitive firm. Market equilibrium is determined by comparing individual firm supply and market demand. [/SUMMARY]
This document provides an overview of pure competition in the short run. It discusses the key characteristics of pure competition including many small firms, standardized products, free entry and exit, and firms being price takers. It then examines the profit maximization process for a competitive firm. A firm will produce where marginal revenue equals marginal cost to maximize profits or minimize losses. The marginal cost curve represents the firm's short-run supply curve. The market supply curve is the horizontal sum of individual firm supply curves. Equilibrium in the market occurs where price equals marginal cost across firms.
- A business firm employs factors of production like resources to produce goods and services that are sold to consumers, other firms, or the government.
- Firms arise when individuals can obtain benefits from working as a team, with managers directing employees and monitoring workers to reduce shirking.
- Exchanges take place inside the firm between individuals forming teams and workers choosing monitors, and outside the firm as the firm sells its products.
This document provides an overview of production processes and profit-maximizing behavior of firms. It discusses key concepts including the production function, total product, marginal product, average product, choice of technology, isoquants, isocosts, and how firms determine their cost-minimizing production method. The document also distinguishes between short-run and long-run decisions and explains how firms make output, technology, and input demand decisions to maximize profits.
This document provides an overview of perfect competition in 3 chapters and sections:
1) The characteristics of perfect competition and why it matters for firms and markets.
2) How perfectly competitive firms determine optimal output levels by producing where marginal revenue equals marginal cost.
3) How firms enter and exit markets in response to economic profits and losses in the long-run to achieve equilibrium with zero profits.
Costs include both explicit costs that require money outlays and implicit costs that do not require money but represent opportunities forgone. Marginal cost is the change in total cost from producing one more unit and is important for profit maximization. In the short run, some costs are fixed while in the long run all costs are variable as firms can adjust all inputs. Economies and diseconomies of scale affect average total cost as the scale of production changes.
Costs Of Production Micro Economics ECO101Sabih Kamran
This document discusses the costs of production for a firm. It begins by defining a firm and its goal of profit maximization. It explains that a firm faces constraints from technology, information, and markets. It also discusses the five basic decisions a firm must make: what and how much to produce, how to produce, how to organize workers, how to market and price products, and what to produce internally vs externally.
The document then explains the differences between short-run and long-run time frames. In the short-run, capital is fixed while variable inputs can change, while in the long-run all inputs are variable. It introduces the concepts of total, average, and marginal costs. Finally, it discusses how
This document discusses Porter's five forces model and different market structures including perfect competition, monopolistic competition, oligopoly, and monopoly. It also defines economies of scale and discusses the Herfindahl-Hirschman Index (HHI) measure of market concentration. Several questions are asked about short run vs long run decisions, the marginal product and average product of labor, and increasing productivity.
The document discusses Porter's five forces model and different market structures. It defines perfect competition, monopolistic competition, oligopoly, and monopoly market structures. It also discusses economies of scale, the four-firm concentration ratio, and the Herfindahl-Hirschman Index (HHI) for measuring market concentration. Several questions are posed about these topics and answered in the document.
Cost-plus pricing: Simplistic strategy that guarantees that price is higher than the estimated average cost
Studies of pricing behavior suggest that many managers who use cost-plus pricing do not price optimally.
Definition of Markup: Markup = (Price – Cost)/Cost where Cost here is cost per unit
The short-run equilibrium in monopolistic competition is Identical to short-run equilibrium under monopoly
As entry and exit of firms from the product group shifts individual firms’ demand curves, long-run equilibrium occurs where profit is equal to zero.
This document provides answers to practice questions about capital budgeting and project valuation using decision trees. It includes sample calculations of NPV and leverage for projects under different scenarios. Decision trees are presented to analyze options like expansion, abandonment, and timing of investment for aircraft purchase projects. The value of real options like abandonment is calculated. Overall, the document demonstrates how to model investment decisions and optionality using decision trees.
The document discusses decision trees, which are diagrams that illustrate decisions and their potential consequences. It provides examples of decision trees used by two companies - Manly Plastics and Vine Desserts - to analyze decisions about new product development and business location selection. It also discusses key concepts in decision trees, including decision nodes, chance nodes, expected value calculations, and how decision trees can be used for regression and survival analysis involving continuous or time-to-event outcomes.
Cost-volume-profit (CVP) analysis is a technique used to analyze the relationship between costs, volume, and profits. It uses linear equations to model how total costs and revenues change with production volume. CVP breaks down costs into fixed and variable components and calculates the break-even point, where total revenues equal total costs. It also determines the contribution margin of each unit and how many units must be sold to cover fixed costs. CVP analysis is useful for short-term decision making but assumes costs and prices remain constant, which limits its effectiveness for long-term planning.
Toy0.1 Model Modification: Introduce Technological Aggregate ShocksKübra Bayram
1) The document describes a toy economic model with firms that produce output based on stochastic shocks and use net worth for production. Introducing dividends that pay out 10% of profits reduces firms' ability to accumulate net worth over time.
2) Analysis found the economy with dividends had lower average production, higher volatility, and a trend toward more unequal net worth distribution compared to the original model.
3) Increasing dividends to 20% caused larger drops in production that took longer to recover from, indicating dividends hinder the ability of firms to overcome economic shocks through capital accumulation.
The document discusses linear programming (LP) and its solution methods. It provides an overview of LP, describing it as a technique for optimization problems where the objective function and constraints are expressed as linear equations. Two common solution methods are then discussed: graphical and simplex. The graphical method involves plotting the constraints on a graph and finding the optimal solution at the corner point of the feasible region. The simplex method is an iterative algebraic approach that moves between basic feasible solutions to optimize the objective function.
The document describes a Monte Carlo simulation process for modeling uncertainty. It provides examples of simulating daily demand for a bakery and a car rental company using random numbers and probability distributions. For the bakery, the average daily demand over 5 days was calculated to be 17 units. For the car rental company, the average number of trips per week over 10 weeks was calculated to be 2.8 trips. The document demonstrates how Monte Carlo simulation can be used to model systems with uncertain variables and calculate average outcomes.
The document discusses the different types of costs that firms face in production. It begins by explaining that total cost is the total amount a firm pays for inputs and is the key determinant of a firm's revenue, pricing, and production decisions. It then defines various types of costs including fixed costs, variable costs, total costs, average costs, and marginal costs. The document also discusses the concepts of economies and diseconomies of scale and how the average total cost curve changes between the short run and long run based on a firm's ability to adjust capacity. Overall, the document provides an overview of cost concepts to understand a firm's production and pricing behavior.
The document discusses decision theory and decision trees. It introduces decision making under certainty, risk, and uncertainty. It defines elements related to decisions like goals, courses of action, states of nature, and payoffs. It also discusses concepts like expected monetary value, expected profit with perfect information, expected value of perfect information, and expected opportunity loss. Examples are provided to demonstrate calculating these metrics. Finally, it provides an overview of how to construct a decision tree, including defining the different node types and how to calculate values within the tree.
Gabinete em Rede | André Lima (Desafio Jovens RAPS 2014)Fernando Holanda
O documento descreve um plano para implementar um "Gabinete em Rede" para um deputado federal, com o objetivo de promover maior transparência, participação cidadã e democracia. O plano inclui realizar seminários e videoconferências, newsletters, redes sociais e ferramentas de colaboração para compartilhar informações e receber feedback do público.
Este documento descreve um plano para estabelecer um centro de reabilitação no Hospital Instituto de Medicina Integral Prof. Fernando Figueira (IMIP) em Recife, Pernambuco. O centro terá uma equipe multidisciplinar para fornecer reabilitação física, ocupacional e outros serviços. Ele será equipado com diversos recursos terapêuticos e contará com a capacitação da equipe. O objetivo é promover a reintegração de pessoas com deficiência na sociedade e no mercado de trabalho.
The document discusses four market structures: pure competition, pure monopoly, monopolistic competition, and oligopoly. It provides details on the characteristics, pricing, and profit maximization analysis of perfect competition and pure monopoly. An example is given to illustrate the cost structure and profit calculation of a perfectly competitive firm. Market equilibrium is determined by comparing individual firm supply and market demand. [/SUMMARY]
This document provides an overview of pure competition in the short run. It discusses the key characteristics of pure competition including many small firms, standardized products, free entry and exit, and firms being price takers. It then examines the profit maximization process for a competitive firm. A firm will produce where marginal revenue equals marginal cost to maximize profits or minimize losses. The marginal cost curve represents the firm's short-run supply curve. The market supply curve is the horizontal sum of individual firm supply curves. Equilibrium in the market occurs where price equals marginal cost across firms.
- A business firm employs factors of production like resources to produce goods and services that are sold to consumers, other firms, or the government.
- Firms arise when individuals can obtain benefits from working as a team, with managers directing employees and monitoring workers to reduce shirking.
- Exchanges take place inside the firm between individuals forming teams and workers choosing monitors, and outside the firm as the firm sells its products.
This document provides an overview of production processes and profit-maximizing behavior of firms. It discusses key concepts including the production function, total product, marginal product, average product, choice of technology, isoquants, isocosts, and how firms determine their cost-minimizing production method. The document also distinguishes between short-run and long-run decisions and explains how firms make output, technology, and input demand decisions to maximize profits.
This document provides an overview of perfect competition in 3 chapters and sections:
1) The characteristics of perfect competition and why it matters for firms and markets.
2) How perfectly competitive firms determine optimal output levels by producing where marginal revenue equals marginal cost.
3) How firms enter and exit markets in response to economic profits and losses in the long-run to achieve equilibrium with zero profits.
Costs include both explicit costs that require money outlays and implicit costs that do not require money but represent opportunities forgone. Marginal cost is the change in total cost from producing one more unit and is important for profit maximization. In the short run, some costs are fixed while in the long run all costs are variable as firms can adjust all inputs. Economies and diseconomies of scale affect average total cost as the scale of production changes.
Costs Of Production Micro Economics ECO101Sabih Kamran
This document discusses the costs of production for a firm. It begins by defining a firm and its goal of profit maximization. It explains that a firm faces constraints from technology, information, and markets. It also discusses the five basic decisions a firm must make: what and how much to produce, how to produce, how to organize workers, how to market and price products, and what to produce internally vs externally.
The document then explains the differences between short-run and long-run time frames. In the short-run, capital is fixed while variable inputs can change, while in the long-run all inputs are variable. It introduces the concepts of total, average, and marginal costs. Finally, it discusses how
This document discusses Porter's five forces model and different market structures including perfect competition, monopolistic competition, oligopoly, and monopoly. It also defines economies of scale and discusses the Herfindahl-Hirschman Index (HHI) measure of market concentration. Several questions are asked about short run vs long run decisions, the marginal product and average product of labor, and increasing productivity.
The document discusses Porter's five forces model and different market structures. It defines perfect competition, monopolistic competition, oligopoly, and monopoly market structures. It also discusses economies of scale, the four-firm concentration ratio, and the Herfindahl-Hirschman Index (HHI) for measuring market concentration. Several questions are posed about these topics and answered in the document.
Cost-plus pricing: Simplistic strategy that guarantees that price is higher than the estimated average cost
Studies of pricing behavior suggest that many managers who use cost-plus pricing do not price optimally.
Definition of Markup: Markup = (Price – Cost)/Cost where Cost here is cost per unit
The short-run equilibrium in monopolistic competition is Identical to short-run equilibrium under monopoly
As entry and exit of firms from the product group shifts individual firms’ demand curves, long-run equilibrium occurs where profit is equal to zero.
This document provides answers to practice questions about capital budgeting and project valuation using decision trees. It includes sample calculations of NPV and leverage for projects under different scenarios. Decision trees are presented to analyze options like expansion, abandonment, and timing of investment for aircraft purchase projects. The value of real options like abandonment is calculated. Overall, the document demonstrates how to model investment decisions and optionality using decision trees.
The document discusses decision trees, which are diagrams that illustrate decisions and their potential consequences. It provides examples of decision trees used by two companies - Manly Plastics and Vine Desserts - to analyze decisions about new product development and business location selection. It also discusses key concepts in decision trees, including decision nodes, chance nodes, expected value calculations, and how decision trees can be used for regression and survival analysis involving continuous or time-to-event outcomes.
Cost-volume-profit (CVP) analysis is a technique used to analyze the relationship between costs, volume, and profits. It uses linear equations to model how total costs and revenues change with production volume. CVP breaks down costs into fixed and variable components and calculates the break-even point, where total revenues equal total costs. It also determines the contribution margin of each unit and how many units must be sold to cover fixed costs. CVP analysis is useful for short-term decision making but assumes costs and prices remain constant, which limits its effectiveness for long-term planning.
Toy0.1 Model Modification: Introduce Technological Aggregate ShocksKübra Bayram
1) The document describes a toy economic model with firms that produce output based on stochastic shocks and use net worth for production. Introducing dividends that pay out 10% of profits reduces firms' ability to accumulate net worth over time.
2) Analysis found the economy with dividends had lower average production, higher volatility, and a trend toward more unequal net worth distribution compared to the original model.
3) Increasing dividends to 20% caused larger drops in production that took longer to recover from, indicating dividends hinder the ability of firms to overcome economic shocks through capital accumulation.
The document discusses linear programming (LP) and its solution methods. It provides an overview of LP, describing it as a technique for optimization problems where the objective function and constraints are expressed as linear equations. Two common solution methods are then discussed: graphical and simplex. The graphical method involves plotting the constraints on a graph and finding the optimal solution at the corner point of the feasible region. The simplex method is an iterative algebraic approach that moves between basic feasible solutions to optimize the objective function.
The document describes a Monte Carlo simulation process for modeling uncertainty. It provides examples of simulating daily demand for a bakery and a car rental company using random numbers and probability distributions. For the bakery, the average daily demand over 5 days was calculated to be 17 units. For the car rental company, the average number of trips per week over 10 weeks was calculated to be 2.8 trips. The document demonstrates how Monte Carlo simulation can be used to model systems with uncertain variables and calculate average outcomes.
The document discusses the different types of costs that firms face in production. It begins by explaining that total cost is the total amount a firm pays for inputs and is the key determinant of a firm's revenue, pricing, and production decisions. It then defines various types of costs including fixed costs, variable costs, total costs, average costs, and marginal costs. The document also discusses the concepts of economies and diseconomies of scale and how the average total cost curve changes between the short run and long run based on a firm's ability to adjust capacity. Overall, the document provides an overview of cost concepts to understand a firm's production and pricing behavior.
The document discusses decision theory and decision trees. It introduces decision making under certainty, risk, and uncertainty. It defines elements related to decisions like goals, courses of action, states of nature, and payoffs. It also discusses concepts like expected monetary value, expected profit with perfect information, expected value of perfect information, and expected opportunity loss. Examples are provided to demonstrate calculating these metrics. Finally, it provides an overview of how to construct a decision tree, including defining the different node types and how to calculate values within the tree.
Gabinete em Rede | André Lima (Desafio Jovens RAPS 2014)Fernando Holanda
O documento descreve um plano para implementar um "Gabinete em Rede" para um deputado federal, com o objetivo de promover maior transparência, participação cidadã e democracia. O plano inclui realizar seminários e videoconferências, newsletters, redes sociais e ferramentas de colaboração para compartilhar informações e receber feedback do público.
Este documento descreve um plano para estabelecer um centro de reabilitação no Hospital Instituto de Medicina Integral Prof. Fernando Figueira (IMIP) em Recife, Pernambuco. O centro terá uma equipe multidisciplinar para fornecer reabilitação física, ocupacional e outros serviços. Ele será equipado com diversos recursos terapêuticos e contará com a capacitação da equipe. O objetivo é promover a reintegração de pessoas com deficiência na sociedade e no mercado de trabalho.
2020 forecasT: the future of cities, information, and inclusionFernando Holanda
over the next decade, cities will continue to grow larger at a rapid pace. at the same time, new technologies will unlock massive streams of data about cities and their residents. as these forces collide, they will turn every city into a unique civic laboratory— a place where technology is adapted in novel ways to meet local needs. This ten-year forecast map charts the important intersections between urbanization and digitalization that will shape this global urban experiment, and the key tensions that will arise.
Jornal do commercio cidades - notícias - “nunca mais pudemos ser o que nós ...Fernando Holanda
1) O Náutico estreou com vitória na Série B do Campeonato Brasileiro de 2010 ao vencer um jogo no domingo, 9 de maio.
2) A matéria entrevista Dirce Just, mãe de Maristela Just que foi assassinada pelo ex-marido em 1989.
3) Dirce espera que o assassino José Ramos seja condenado no julgamento após 21 anos, trazendo justiça para a família.
Jornal do commercio cidades - notícias - à espera de uma justiça que tardou...Fernando Holanda
O documento relata o caso de Maristela Just, uma universitária assassinada pelo ex-marido em 1989. Após 21 anos, o julgamento do assassino finalmente ocorrerá na próxima quinta-feira. Os filhos de Maristela, agora adultos, testemunharão contra o pai no julgamento. A família aguarda por justiça e espera que o assassino seja condenado.
O documento descreve um caso de assassinato ocorrido em 1989 no qual José Ramos Lopes Neto matou sua ex-mulher Maristela Just e feriu os filhos do casal e o cunhado. Após 21 anos, o caso finalmente irá a júri popular em maio de 2010, para que a família possa enfim obter justiça. A mídia tem acompanhado o caso ao longo dos anos.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise boosts blood flow, releases endorphins, and promotes changes in the brain which help relax the body and lift the mood.
This chapter introduces marketing metrics and their importance. It defines a metric as a measuring system that quantifies trends, dynamics, or characteristics. Metrics are crucial for marketers as they encourage rigor, objectivity, and accountability. They allow marketers to measure performance, compare results over time and across contexts, and identify opportunities for improvement. Understanding key marketing metrics is essential for effective decision-making, strategy evaluation, and performance management.
This chapter introduces marketing metrics and their importance. It defines a metric as a measuring system that quantifies trends, dynamics, or characteristics. Metrics are crucial for marketers as they encourage rigor, objectivity, and accountability. They allow marketers to measure performance, compare results over time and across areas, and identify opportunities for improvement. Understanding key marketing metrics is essential for effective decision-making, strategy evaluation, and performance management.
A empresa de tecnologia anunciou um novo smartphone com câmera aprimorada, tela maior e bateria de longa duração por um preço acessível. O dispositivo tem como objetivo atrair mais consumidores em mercados emergentes com suas especificações equilibradas e preço baixo. Analistas esperam que as melhorias e o preço baixo impulsionem as vendas do novo aparelho.
Determinantes na satisfação de clientes em hotéis de cinco estrelas em Por...Fernando Holanda
Este documento resume um estudo sobre os determinantes da satisfação dos clientes em hotéis de cinco estrelas em Portugal. O estudo analisou amostras de clientes de oito hotéis e usou um modelo de regressão ordinal para identificar os atributos que mais influenciam a satisfação geral. Os resultados mostraram que os funcionários, o conforto e o preço são os três principais determinantes da satisfação geral dos clientes em hotéis de luxo em Portugal.
The document discusses the results of a study on the impact of COVID-19 lockdowns on air pollution. The study found that lockdowns led to significant short-term reductions in nitrogen dioxide and fine particulate matter pollution globally as human activity declined. However, the improvements were temporary and air quality returned to pre-pandemic levels as restrictions eased and activity increased again.
Este documento discute um modelo teórico e proposições de pesquisa sobre os antecedentes da lealdade de clientes empresariais no contexto bancário. Propõe um modelo onde a lealdade é influenciada por emoções, qualidade do relacionamento, satisfação, confiança, comprometimento afetivo, custos de mudança e dependência. Argumenta que variáveis emocionais podem influenciar a lealdade de clientes empresariais a bancos, ao contrário do que sugerem apenas variáveis cognitivas.
1) O PIB brasileiro caiu 0,2% em 2009, mas poderia ter caído mais de 7% sem as políticas anticíclicas do governo, como redução de tributos e aumento dos gastos públicos.
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3) A Anvisa regulamentou o uso de plantas medicinais da tradição popular, exigindo boas práticas de
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(1) Os indicadores econômicos da zona euro e da União Europeia continuaram a melhorar em dezembro, embora ainda abaixo das médias históricas.
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This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
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Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...indexPub
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
1. OR-Notes
J E Beasley
OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of
operations research (OR). They were originally used by me in an introductory OR course I give at
Imperial College. They are now available for use by any students and teachers interested in OR
subject to the following conditions.
A full list of the topics available in OR-Notes can be found here.
Decision trees
Introduction
In many problems chance (or probability) plays an important role. Decision analysis is the general
name that is given to techniques for analysing problems containing risk/uncertainty/probabilities.
Decision trees are one specific decision analysis technique and we will illustrate the technique by
use of an example.
Example
A company faces a decision with respect to a product (codenamed M997) developed by one of its
research laboratories. It has to decide whether to proceed to test market M997 or whether to drop it
completely. It is estimated that test marketing will cost £100K. Past experience indicates that only
30% of products are successful in test market.
If M997 is successful at the test market stage then the company faces a further decision relating to
the size of plant to set up to produce M997. A small plant will cost £150K to build and produce 2000
units a year whilst a large plant will cost £250K to build but produce 4000 units a year.
The marketing department have estimated that there is a 40% chance that the competition will
respond with a similar product and that the price per unit sold (in £) will be as follows (assuming all
production sold):
Large plant Small plant
Competition respond 20 35
Competition do not respond 50 65
Assuming that the life of the market for M997 is estimated to be 7 years and that the yearly plant
running costs are £50K (both sizes of plant - to make the numbers easier!) should the company go
ahead and test market M997?
Solution
Although the above example is somewhat simplified it plainly represents the type of decision that
often has to be made about new products.
2. In particular note how we cannot separate the test market decision from any decisions about
the future profitability (if any) of the product if test marketing is successful.
To enable us to see what is going on consider the figure below where we have drawn the decision
tree for the problem.
In that figure we have three types of node represented:
decision nodes;
chance nodes; and
terminal nodes.
Decision nodes represent points at which the company has to make a choice of one alternative from
a number of possible alternatives e.g. at the first decision node the company has to choose one of the
two alternatives "drop M997" or "test market M997".
Chance nodes represent points at which chance, or probability, plays a dominant role and reflect
alternatives over which the company has (effectively) no control.
Terminal nodes represent the ends of paths from left to right through the decision tree.
It is worth saying here that the difficult part of the decision tree technique is drawing up a
diagram such as the figure above from the written description of the problem. Once that has
been done the solution procedure is quite straightforward. Note here that most, but not all,
decision trees start with a decision node. One tip that may help you to draw decision trees is to
ask yourself the question "What happens next?" at each point in the tree as you draw it.
3. Note here the inclusion of the "no plant" alternative at the plant size decision node. This is necessary
because it simply may not be profitable to build any plant (large or small) even if the product is
successful in test market. It is common in decision tree problems to find that at decision nodes we
need a "do nothing" alternative which is an implicit decision that can be taken.
Note that it is important for the decision tree to be drawn so that there is a unique path in the tree
from the initial node to each of the terminal nodes.
To ease the discussion of the decision tree we have numbered the nodes (decision/chance/terminal)
1,2,3,...,12. At each decision node we have also numbered the alternatives, at node 1 we have
alternatives 1 and 2 and at node 5 alternatives 3, 4 and 5.
Although the decision tree diagram does help us to see more clearly the nature of the problem it has
not, so far, helped us to decide whether to drop M997 or whether to test market it (the decision we
are trying to make!). To do this we have two steps as illustrated below.
In these steps we will need to use information (numbers) relating to future sales, prices, costs,
etc. Whilst we may not be able to give accurate figures for these we need to factor such figures
into our calculations if we are to proceed. Investigating how our decision to test market or not
might change as these figures change (i.e. sensitivity analysis) can be done once we have
carried out the basic calculations using our assumed figures.
Step 1
In this step we, for each path through the decision tree from the initial node to a terminal node of a
branch, work out the profit (in £) involved in that path. Essentially in this step we work from the
left-hand side of the diagram to the right-hand side.
path to terminal node 2 - we drop M997
Total revenue = 0
Total cost = 0
Total profit = 0
Note that we ignore here (and below) any money already spent on developing M997 (that being
a sunk cost, i.e. a cost that cannot be altered no matter what our future decisions are, so
logically has no part to play in deciding future decisions).
path to terminal node 4 - we test market M997 (cost £100K) but then find it is not successful
so we drop it
Total revenue = 0
Total cost = 100
Total profit = -100 (all figures in £K)
path to terminal node 7 - we test market M997 (cost £100K), find it is successful, build a
small plant (cost £150K) and find we are without competition (revenue for 7 years at 2000
units a year at £65 per unit = £910K)
Total revenue = 910
4. Total cost = 250 + 7x50 (running cost)
Total profit = 310
path to terminal node 8 - we test market M997 (cost £100K), find it is successful, build a
small plant (cost £150K) and find we have competition (revenue for 7 years at 2000 units a
year at £35 per unit = £490K)
Total revenue = 490
Total cost = 250 + 7x50
Total profit = -110
path to terminal node 10 - we test market M997 (cost £100K), find it is successful, build a
large plant (cost £250K) and find we are without competition (revenue for 7 years at 4000
units a year at £50 per unit = £1400K)
Total revenue = 1400
Total cost = 350 + 7x50
Total profit = 700
path to terminal node 11 - we test market M997 (cost £100K), find it is successful, build a
large plant (cost £250K) and find we have competition (revenue for 7 years at 4000 units a
year at £20 per unit = £560K)
Total revenue = 560
Total cost = 350 + 7x50
Total profit = -140
path to terminal node 12 - we test market M997 (cost £100K), find it is successful, but decide
not to build a plant
Total revenue = 0
Total cost = 100
Total profit = -100
Note that, as mentioned previously, we include this option because, even if the product is successful
in test market, we may not be able to make sufficient revenue from it to cover any plant construction
and running costs.
Hence we can form the table below indicating, for each branch, the total profit involved in that
branch from the initial node to the terminal node.
Terminal node Total profit (£K)
2 0
4 -100
7 310
8 -110
10 700
11 -140
12 -100
So far we have not made use of the probabilities in the problem - this we do in the second step
where we work from the right-hand side of the diagram back to the left-hand side.
5. Step 2
Consider chance node 6 with branches to terminal nodes 7 and 8 emanating from it. The branch to
terminal node 7 occurs with probability 0.6 and total profit 310K whilst the branch to terminal node
8 occurs with probability 0.4 and total profit -110K. Hence the expected monetary value (EMV) of
this chance node is given by
0.6 x (310) + 0.4 x (-110) = 142 (£K)
Essentially this figure represents the expected (or average) profit from this chance node (60% of the
time we get £310K and 40% of the time we get -£110K so on average we get (0.6 x (310) + 0.4 x
(-110)) = 142 (£K)).
The EMV for any chance node is defined by "sum over all branches, the probability of the branch
multiplied by the monetary (£) value of the branch". Hence the EMV for chance node 9 with
branches to terminal nodes 10 and 11 emanating from it is given by
0.6 x (700) + 0.4 x (-140) = 364 (£K)
node 10 node 11
We can now picture the decision node relating to the size of plant to build as below where the
chance nodes have been replaced by their corresponding EMV's.
Hence at the plant decision node we have the three alternatives:
Alternative 3: build small plant EMV = 142K
Alternative 4: build large plant EMV = 364K
Alternative 5: build no plant EMV = -100K
It is clear that, in £ terms, alternative number 4 is the most attractive alternative and so we can
discard the other two alternatives, giving the revised decision tree shown below.
6. We can now repeat the process we carried out above.
The EMV for chance node 3 representing whether M997 is a success in test market or not is given
by
0.3 x (364) + 0.7 x (-100) = 39.2 (£K)
plant decision node node 4
Hence at the decision node representing whether to test market M997 or not we have the two
alternatives:
Alternative 1: drop M997 EMV = 0
Alternative 2: test market M997 EMV = 39.2K
It is clear that, in £ terms, alternative number 2 is preferable and so we should decide to test market
M997.
Summary
Let us be clear then about what we have decided as a result of the above process:
we should test market M997 and this decision has an expected monetary value (EMV) of
£39.2K
if M997 is successful in test market then we anticipate, at this stage, building a large plant
(recall the alternative we chose at the decision node relating to the size of plant to build).
However it is plain that in real life we will review this once test marketing has been
completed.
Note here that the EMV of our decision (39.2 in this case) DOES NOT reflect what will
actually happen - it is merely an average or expected value if we were to have the tree many
times - but if fact we have the tree once only. If we follow the path suggested above of test
marketing M997 then the actual monetary outcome will be one of [-100, 310, -110, 700, -140,
-100] corresponding to terminal nodes 4,7,8,10,11 and 12 depending upon future decisions and
7. chance events.
Upside and downside
Conceptually one can think of the set of terminal nodes that can be reached as a result of our test
market decision as the set of possible futures. The best possible future corresponding to the decision
to test market M997 is called the upside and the worst possible future corresponding to the decision
to test market M997 is called the downside.
We need to be slightly careful here since, as noted above, the actual monetary outcomes will depend
both upon future decisions and chance events.
If we are committed to a large plant (assuming we are successful in test market) then the set of
possible futures is given by [-100, 700, -140] corresponding to terminal nodes 4,10 and 11 and
hence the upside is 700 (£K) and the downside is -140 (£K).
If we are not committed to a large plant (assuming we are successful in test market) then the set of
possible futures is given by [-100, 310, -110, 700, -140, -100] corresponding to terminal nodes
4,7,8,10,11 and 12 and hence the upside is 700 (£K) and the downside is -140 (£K).
Whilst in this particular example the upside and downside are the same irrespective of whether we
are committed to a large plant or not note how the possible futures are different depending upon
whether we are committed to a large plant or not.
Package solution
The above problem was solved using the package, the input being shown below. The description of
the input is as follows. All data is entered by nodes in the tree. Each node has a type (d for decision
nodes and c for chance nodes), or is left blank for terminal nodes. All following nodes in the
decision tree are listed.
If a node comes from a chance node then it has a non-zero probability value assigned. If the node is
a terminal node then a payoff/cost is also assigned.
8. In the output shown below we have for each decision node the expected value and the appropriate
decision and for each chance node the expected value.
It is clear that the package agrees with the calculation we carried out before.
Note here that this package is also capable of drawing the tree for use from the input, so we can
check we have entered it correctly), as below.
Note here that since the decision tree calculation is so straightforward it is relatively easy to conduct
sensitivity analysis to see how the recommended course of action changes (if at all) in response to
data changes.
Sensitivity analysis
Consider the decision tree given above. It is plain that the decision to test market is influenced by the
profit of 700 (£K) that we will get if test marketing is successful and we choose to build a large plant
and we find that we have no competition. Colloquially we could say that we are "following the
money". Hence we may vary this figure of 700 (and/or vary the probability that this outcome occurs)
to see if it changes the test market decision.
9. For example, suppose the probability that we have no competition with a large plant is no longer 0.6
but is instead 0.45. This implies that the probability that we have competition is hence 1-0.45=0.55.
Redoing the decision tree calculation (here using the package) we get:
Hence we can see that the initial decision (to test market) is still the optimal decision.
We can also conduct sensitivity analysis using a more systematic algebraic basis (i.e. assign a
symbol p to a given probability and work out algebraic expressions for EMVs). To see this suppose
that the probability of competition with a large plant is no longer 0.6 but is instead p. This implies
that the probability that we have competition is hence 1-p. Assume that we can leave the
probabilities for a small plant of competition/no competition unaltered. It is clear that as p decreases
we will at some stage prefer a small plant over a large plant (e.g. if p=0 then a small plant with EMV
of 142 would be preferable to a large plant with EMV of -140). We can therefore ask the logical
question "How small does p have to be before we prefer a small plant?"
To answer this question we have that we will be indifferent between a small and a large plant when
their EMVs are equal, i.e. when
p(700) + (1-p)(-140) = 142
i.e. when 840p - 140 = 142, so p = 282/840 = 0.3357
Hence if p drops below 0.3357 we would prefer a small plant to a large plant. This type of
systematic sensitivity analysis can be preferable in some circumstances to simply trying different
10. numbers and redoing the calculation to see what the effect is.
Extensions
The basic decision tree technique presented above can be applied to any problem for which a
decision tree can be drawn. There are a number of extensions to the technique and we briefly
consider four such extensions below. These relate to:
discounting
chance nodes
decision nodes
utility.
We consider each in turn.
Discounting
In the example given above we were concerned with money received over 7 years. It is plain that £1
received in seven years time is worth less than £1 received now and a technique called discounting,
or discounted cash flow, (involving finding the net present value of any sum of money) can be used
to overcome this difficulty. Applying discounting merely alters the numbers which are fed into the
decision tree so that we are dealing with monetary values on an equivalent (present-day) basis. It
does not effect the processing of the tree (which remains exactly as indicated above).
Chance nodes
In the example given above we calculated a value for each chance node. Whilst we have used EMV
as the value of a chance node this choice is, in many respects, somewhat arbitrary and other ways of
calculating a value for a chance node have been suggested. To put it another way whilst it is a law of
the universe (in this particular corner of the space-time continuum) that E=mc2 it is not a law of the
universe that the value of a chance node must be the equal to the EMV value!
Reflect that EMV is an average value - but at a chance node we never see the average - something
happens once only (e.g. at chance node 6 we either see competition or not). Hence perhaps the
average value is misleading and we need to look at a chance node a different way.
If we were adverse to losing money and wished to take a conservative attitude to decision making
(risk) we might calculate the value of a chance node as the worst possible outcome that might occur
at that node. Such a strategy is often called a pessimistic strategy (e.g. such a strategy would assign
chance node 6 a value of -110 compared with an EMV of 142).
An alternative strategy would be the optimistic strategy of calculating the value of a chance node as
the best possible outcome that might occur at that node (e.g. such a strategy would assign chance
node 6 a value of 310 compared with an EMV of 142).
Yet another strategy would be to take the value of a chance node as equal to the most likely (highest
probability) outcome that might occur at that node (e.g. such a strategy would assign chance node 4
a value of 310 compared with an EMV of 142).
Alternatively we might take the value of a chance node to be some weighted combination of the
11. EMV and the values given by the optimistic and pessimistic strategies. The literature contains a
number of variations on this theme of changing the value of a chance node.
Decision nodes
At each decision node we choose one of the alternative decisions at that node based upon an implicit
rule ("choose the alternative with the highest EMV"). Other rules are equally plausible (e.g. "choose
the alternative with the highest ROI" (ROI = return on investment = profit divided by total
investment)).
For example consider the small and large plants above. We saw that a small plant led to an EMV
(actually an expected net profit) of 142. That involved a total investment of 100 for test marketing
plus 150 to build, so a ROI of 142/(100+150) = 56.8%
A large plant led to an EMV (actually an expected net profit) of 364. That involved a total
investment of 100 for test marketing plus 250 to build, so a ROI of 364/(100+250) = 104%
Whilst, in this case ROI would lead to the same decision relating to the size of plant to build it could
have led to a different decision. For example had the EMV at chance node 9 been 175 then on an
EMV basis we would still have chosen at decision node 5 to build a large plant. But on a ROI basis
[175/(100+250) = 50%] we would chose to build a small plant.
Utility
Using monetary values in the decision tree implies, for example, that a loss of 200K is only twice as
bad as a loss of 100K. If the company doesn't have 200K to lose, but does have 100K, then it is plain
that they will regard losing 200K as much worse than losing 100K. Moreover note that often
decisions are made by people within the company. The company makes the profit/loss, not the
people concerned with the decision.
Hence the idea of utility is to replace the monetary values at each terminal node in the decision tree
by utilities (points) which reflect the view of the decision maker (or company) to that sum of money
(e.g. a loss of 100K might get a utility value of -5 but a loss of 200K a utility value of -500). In
simple terms you can think of utilities as replacing £'s by points.
Trying to capture the decision-maker's translation of £'s to points is an imprecise process, but it does
enable the decision-maker's valid view of the problem in terms of the importance of £'s to them to be
incorporated. Once utility values have been found then we proceed as before.
Some more decision tree examples can be found here.