Inputs output costs

Marginal Analysis, Inputs, Output & Costs [email_address]

We ’ll try to learn about:
Marginal analysis (marginal costs & benefits)
Total, marginal & average quantities
Production function
Fixed & variable inputs
Diminishing returns (i.e. decreasing marginal output)
Fixed & variable cost, total cost, marginal & average cost
Short-term & long-term costs
Returns to scale

Opportunity Cost
The opportunity cost of an action (buying or selling, consuming or producing) is the sum of explicit and implicit costs.
An explicit cost is a cost that involves actually laying out money.
An implicit cost does not require an outlay of money; it is measured by the value in dollars of the benefits that are forgone.

Opportunity Cost of an Additional Year of School

Accounting Profit vs. Economic Profit
The accounting profit of a business is the business ’s revenue minus the explicit costs (including depreciation).
The economic profit of a business is the business ’s revenue minus the opportunity cost of its inputs
Usually, economic profit < accounting profit.

Capital
The capital of a business is the value of its assets.
The implicit cost of capital is the opportunity cost of the capital used by a business.
Usually, the opportunity cost of capital is the interest that a business ’ capital would gain otherwise.

Profits at B ’s Cafe

Marginal Cost The marginal cost of producing a good is the additional cost incurred by producing one more unit of that good.

Example: Constant Marginal Cost
For every additional chicken wing per serving, Babette ’s marginal cost is $0.80. Babette’s portion size decision is characterized by a constant marginal cost: each chicken wing costs the same amount to produce as the previous one.
Production of a good has constant marginal cost when each additional unit costs the same to produce as the previous one.

Marginal Cost 7 6 5 4 3 2 1 0 $4.00 3.00 2.00 1.00 Marginal cost (per wing) Quantity of chicken wings Marginal cost curve, MC

Marginal Benefit
The marginal benefit of producing a good is the additional benefit earned from producing one more unit of that good.

Marginal Cost - Marginal Benefit
The cost of producing one more unit (MC) depends on the quantity already being produced.
Increasing , constant, decreasing (unusual) MC
The additional benefit derived from producing one more unit of that good (MB)
Decreasing , constant, increasing (unusual) MB

Decreasing Marginal Benefit
Each additional lawn mowed produces less benefit than the previous lawn  with decreasing marginal benefit, each additional unit produces less benefit than the unit before.
There is decreasing marginal benefit from an activity when each additional unit of the activity produces less benefit than the previous unit.

Marginal Benefit 7 6 5 4 3 2 1 0 Marginal benefit curve, MB Marginal cost (per wing) Quantity of chicken wings

Felix ’s Net Gain from Mowing Lawns

Marginal Analysis
The optimal quantity is the quantity that generates the maximum possible total net gain.
The principle of marginal analysis says that the optimal quantity is the quantity at which marginal benefit is equal to marginal cost.
If the good is ‘lumpy’ (not divisible), then the optimal quantity is that at which the marginal benefit is just slightly greater than the marginal cost.

B ’s net gain from increasing portion size

B ’s optimal portion size 7 6 5 4 3 2 1 0 $4.00 3.00 2.00 1.00 Marginal benefit (marginal cost per wing) Quantity of chicken wings Optimal point MC MB Optimal quantity 0 1 2 3 4 5 6 7 Total net gain (profit per serving) Net gain (per wing) Quantity of chicken wings $0 3.50 5.20 5.90 6.30 6.40 6.30 6.10 $3.50 1.70 0.70 0.40 0.10 – 0.10 – 0.20

Sunk Cost
A sunk cost is a cost that has already been incurred and is non-recoverable. A sunk cost should be ignored in decisions about future actions.
Sunk costs should be ignored in making decisions about future actions.
They have already been incurred and are non-recoverable, they have no effect on future costs and benefits.

Production Function
The production function is the relationship between the quantity of inputs a firm uses and the quantity of output it produces (the graph of the production function is called the “total output curve”)
A fixed input is an input whose quantity is fixed for a period of time and cannot be varied.
A variable input is an input whose quantity the firm can vary at any time.

Inputs and Output
Long run: time period in which all inputs can be varied.
Short run: time period in which at least one input is fixed.
Total product curve shows how the quantity of output depends on the quantity of the variable input, for a given quantity of the fixed input.

Production function (total output curve) for a farm 0 1 2 3 4 5 6 7 8 19 17 15 13 11 9 7 5 0 19 36 51 64 75 84 91 96 Quantity of labor L (worker) Quantity of wheat Q (bushels) MP of labor MPL =  Q /  L (bushels per worker) 7 8 6 5 4 3 2 1 0 100 80 60 40 20 Quantity of wheat (bushels) Quantity of labor (workers) Total product, TP Adding a 7 th worker leads to an increase in output of only 7 bushels Adding a 2 nd worker leads to an increase in output of only 17 bushels

The marginal product of an input is the additional quantity of output that is produced by using one more unit of that input (marginal output due to labor).
Marginal Product of Labor

Diminishing Returns to an Input
There are diminishing returns to an input when an increase in the quantity of that input, holding the levels of all other inputs fixed, leads to a decline in the marginal product of that input.

Marginal Product of Labor Curve Marginal product of labor, MPL 7 8 6 5 4 3 2 1 0 19 17 15 13 11 9 7 5 Marginal product of labor (bushels per worker) Quantity of labor (workers) There are diminishing returns to labor.

(a) Total Product Curves (b) Marginal Product Curves Marginal product of labor (bushels per worker) Quantity of wheat (bushels) 7 8 6 5 4 3 2 1 0 30 25 20 15 10 5 7 8 6 5 4 3 2 1 0 160 140 120 100 80 60 40 20 TP 20 TP 10 MPL 20 MPL 10 Quantity of labor (workers) Quantity of labor (workers) Total Product, Marginal Product, and the Fixed Input

From the Production Function to Cost Curves
A fixed cost is a cost that does not depend on the quantity of output produced. It is the cost of the fixed input.
A variable cost is a cost that depends on the quantity of output produced. It is the cost of the variable input.

Total Cost Curve
The total cost of producing a given quantity of output is the sum of the fixed cost and the variable cost of producing that quantity of output.
TC = FC + VC
The total cost curve becomes steeper as more output is produced due to diminishing returns.

Total Cost Curve: G&M ’s Farm 19 36 51 64 75 84 91 96 0 $2,000 1,800 1,600 1,400 1,200 1,000 800 600 400 200 Cost Quantity of wheat (bushels) A B C D E F G Total cost, TC H I A B C D E F G H I Point on graph 0 1 2 3 4 5 6 7 8 $400 400 400 400 400 400 400 400 400 O 200 400 600 800 1,000 1,200 1,400 1,600 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 0 19 36 51 64 75 84 91 96 Variable cost (VC) Total cost (TC = FC + VC) $ $ Quantity of labor L (worker) Quantity of wheat Q (bushels) Fixed Cost (FC)

Two Key Concepts: Marginal Cost and Average Cost As in the case of marginal product, marginal cost is equal to “ rise ” (the increase in total cost) divided by “ run ” (the increase in the quantity of output).

Costs at Selena ’s Gourmet Salsas

TC & MC Curves for Selena ’s Gourmet Salsas $250 200 150 100 50 Cost of case 7 8 9 10 6 5 4 3 2 1 0 $1,400 1,200 1,000 800 600 400 200 Cost Quantity of salsa (cases) 7 8 9 10 6 5 4 3 2 1 0 (b) Marginal Cost (a) Total Cost T C MC Quantity of salsa (cases) 8 th case of salsa increases total cost by $180. 2 nd case of salsa increases total cost by $36.

Why is the Marginal Cost Curve Upward Sloping?
Because there are diminishing returns to inputs in this example. As output increases, the marginal product of the variable input declines.
This implies that more and more of the variable input must be used to produce each additional unit of output as the amount of output already produced rises.
And since each unit of the variable input must be paid for, the cost per additional unit of output also rises.

Average Cost
Average total cost , often referred to simply as average cost , is total cost divided by quantity of output produced.
ATC = TC/Q = (Total Cost) / (Quantity of Output)
A U-shaped average total cost curve falls at low levels of output, then rises at higher levels.
Average fixed cost is the fixed cost per unit of output.
AFC = FC/Q = (Fixed Cost) / (Quantity of Output)

Average Cost
Average variable cost is the variable cost per unit of output.
AVC = VC/Q= (Variable Cost) / (Quantity of Output)

Average Total Cost Curve
Increasing output has two opposing effects on average total cost:
The spreading effect : the larger the output, the greater the quantity of output over which fixed cost is spread, leading to lower the average fixed cost.
The diminishing returns effect : the larger the output, the greater the amount of variable input required to produce additional units leading to higher average variable cost.

AC for Selena ’s Gourmet Salsas

ATC Curve for Selena ’s Gourmet Salsas Average total cost, ATC M 7 8 9 10 6 5 4 3 2 1 0 $140 120 100 80 60 40 20 Minimum average total cost Minimum-cost output Cost of case Quantity of salsa (cases)

Putting the Four Cost Curves Together
Note that:
Marginal cost is upward sloping due to diminishing returns.
Average variable cost also is upward sloping but is flatter than the marginal cost curve.
Average fixed cost is downward sloping because of the spreading effect.
The marginal cost curve intersects the average total cost curve from below, crossing it at its lowest point. This last feature is our next subject of study.

MC and AC Curves for Selena ’s Gourmet Salsas $250 200 150 100 50 7 8 9 10 6 5 4 3 2 1 M 0 MC A T C A VC AFC Minimum-cost output Cost of case Quantity of salsa (cases)

Facts
The minimum-cost output is the quantity of output at which average total cost is lowest — the bottom of the U-shaped average total cost curve.
At the minimum-cost output, average total cost is equal to marginal cost.
At output less than the minimum-cost output, marginal cost is less than average total cost and average total cost is falling.
And at output greater than the minimum-cost output, marginal cost is greater than average total cost and average total cost is rising.

Relationship between ATC and the MC Curves Cost of unit Quantity MC A T C MC L MC H A 1 B 1 A 2 B 2 M If marginal cost is above average total cost, average total cost is rising. If marginal cost is below average total cost, average total cost is falling.

Does the Marginal Cost Curve Always Slope Upward?
In practice, marginal cost curves often slope downward as a firm increases its production from zero up to some low level, sloping upward only at higher levels of production.
This initial downward slope occurs because a firm that employs only a few workers often cannot reap the benefits of specialization of labor. This specialization can lead to increasing returns at first, and so to a downward-sloping marginal cost curve.
Once there are enough workers to permit specialization, however, diminishing returns set in.

More realistic cost curves MC A T C A VC Cost of unit Quantity 2. … but diminishing returns set in once the benefits from specialization are exhausted and marginal cost rises. 1. Increasing specialization leads to lower marginal cost…

Short-Run versus Long-Run Costs
In the short run, fixed cost is completely outside the control of a firm. But all inputs are variable in the long run.
The firm will choose its fixed cost in the long run based on the level of output it expects to produce.

Choosing the FC $250 200 150 100 50 Cost of case Quantity of salsa (cases) 7 8 9 10 6 5 4 3 2 1 0 High fixed cost Low fixed cost A T C 2 A T C 1 At low output levels, low fixed cost yields lower average total cost At high output levels, high fixed cost yields lower average total cost A T C 1 12 48 108 192 300 432 588 768 972 1,200 $ 120 156 216 300 408 540 696 876 1,080 1,308 Total cost $ A T C 2 6 24 54 96 150 216 294 384 486 600 $ $222 240 270 312 366 432 510 600 702 816 Low fixed cost (FC = $108) High fixed cost (FC = $216) $120.00 78.00 72.00 75.00 81.60 90.00 99.43 109.50 120.00 130.80 $222.00 120.00 90.00 78.00 73.20 72.00 72.86 75.00 78.00 81.60 1 2 3 4 5 6 7 8 9 10 Average total cost of case Quantity of salsa (salsa) High variable cost Low variable cost Total cost Average total cost of case

The long-run average total cost curve shows the relationship between output and average total cost when fixed cost has been chosen to minimize average total cost for each level of output.
Long-run ATC curve

Short-Run and Long-Run ATC Curves B A T C 6 A T C 9 A T C 3 L R A T C 3 5 8 4 7 0 6 9 Increasing returns to scale Decreasing returns to scale Constant returns to scale C X A Y Cost of case Quantity of salsa (cases)

Returns to Scale
There are increasing returns to scale (economies of scale) when long-run average total cost declines as output increases.
There are decreasing returns to scale ( diseconomies of scale) when long-run average total cost increases as output increases.
There are constant returns to scale when long-run average total cost is constant as output increases.

Summary
Marginal analysis involves comparing the benefit to the cost of doing an additional unit of an activity. The marginal cost of producing a good is the additional cost incurred by producing one more unit of that good. The marginal benefit of producing a good is the additional benefit earned by producing one more unit.
With constant marginal cost , each additional unit costs the same amount to produce as the unit before; this is represented by a horizontal MC curve. With increasing marginal cost , each unit costs more to produce than the unit before. In the case of decreasing marginal benefit , each additional unit produces a smaller benefit than the unit before.

Summary
According to the principle of marginal analysis , the optimal quantity is the quantity at which MC=MB.
A cost that has already been incurred and that is nonrecoverable is a sunk cost .

Summary
The relationship between inputs and output is a producer ’s production function . In the short run , the quantity of a fixed input cannot be varied but the quantity of a variable input can. In the long run , the quantities of all inputs can be varied. For a given amount of the fixed input, the tota l product curve shows how the quantity of output changes as the quantity of the variable input changes.
There are diminishing returns to an input when its marginal product declines as more of the input is used, holding the quantity of all other inputs fixed.
Total cost is equal to the sum of fixed cost , which does not depend on output, and variable cost , which does depend on output.

Summary
All economic decisions involve the allocation of scarce resources. Some decisions are “either–or” decisions, other decisions are “how much” decisions.
The cost of using a resource for a particular activity is the opportunity cost of that resource. Some opportunity costs are explicit costs ; they involve a direct payment of cash. Other opportunity costs, however, are implicit costs ; they involve no outlay of money but represent the inflows of cash that are forgone. Companies use capital and their owners ’ time. So companies should base decisions on economic profit , which takes into account implicit costs such as the opportunity cost of the owners’ time and the implicit cost of capital .

Summary
Average total cost , total cost divided by quantity of output, is the cost of the average unit of output, and marginal cost is the cost of one more unit produced. U-shaped average total cost curves are typical, because average total cost consists of two parts: average fixed cost , which falls when output increases (the spreading effect), and average variable cost , which rises with output (the diminishing returns effect).
When average total cost is U-shaped, the bottom of the U is the level of output at which average total cost is minimized, the point of minimum-cost output . This is also the point at which the marginal cost curve crosses the average total cost curve from below.

Summary
In the long run, a producer can change its fixed input and its level of fixed cost. The long-run average total cost curve shows the relationship between output and average total cost when fixed cost has been chosen to minimize average total cost at each level of output.
As output increases, there are increasing returns to scale if long-run average total cost declines; decreasing returns to scale if it increases; and constant returns to scale if it remains constant. Scale effects depend on the technology of production.

Inputs output costs

by Julio Huato

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