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Cost theory and analysis

Cost theory and analysis

- 1. COST THEORY AND ANALYSIS MANAGERIAL ECONOMICS
- 2. Costs Theory and Analysis Short run – Diminishing marginal returns results from adding successive quantities of variable factors to a fixed factor Long run – Increases in capacity can lead to increasing, decreasing or constant returns to scale
- 3. Short Run Production Costs Total variable cost (TVC) Total amount paid for variable inputs Increases as output increases Total fixed cost (TFC) Total amount paid for fixed inputs Does not vary with output Total cost (TC) TC = TVC + TFC
- 4. Short-Run Total Cost Schedules Output (Q) Total fixed cost (TFC) taka Total variable cost (TVC) Taka Total Cost Taka TC=TFC+TVC) 0 6,000 100 6,000 200 6,000 300 6,000 400 6,000 500 6,000 600 6,000 0 14,000 22,000 4,000 6,000 9,000 34,000 6,000 20,000 28,000 10,000 12,000 15,000 40,000
- 5. Total Cost Curves
- 6. Average Costs TVC AVC Q TFC AFC Q TC ATC AVC AFC Q • ( AFC ) Average fixed cost • ( ATC ) Average total cost ( AVC ) Average variable cost •
- 7. Short Run Marginal Cost Short run marginal cost (SMC) measures rate of change in total cost (TC) as output varies TC TVC SMC Q Q
- 8. Average & Marginal Cost Schedules Output (Q) Average fixed cost (AFC=TFC/Q) Average variable cost (AVC=TVC/Q) Average total cost (ATC=TC/Q= AFC+AVC) Short-run marginal cost (SMC=TC/Q) 0 100 200 300 400 500 600 -- 15 12 60 30 20 10 -- 35 44 40 30 30 56.7 -- 50 56 100 60 50 66.7 -- 50 80 40 20 30 120
- 9. Average & Marginal Cost Curves
- 10. Short Run Average & Marginal Cost Curves
- 11. Short Run Cost Curve Relations AFC decreases continuously as output increases Equal to vertical distance between ATC & AVC AVC is U-shaped Equals SMC at AVC’s minimum ATC is U-shaped Equals SMC at ATC’s minimum
- 12. Short Run Cost Curve Relations SMC is U-shaped Intersects AVC & ATC at their minimum points Lies below AVC & ATC when AVC & ATC are falling Lies above AVC & ATC when AVC & ATC are rising
- 13. In the case of a single variable input, short-run costs are related to the production function by two relations Relations Between Short-Run Costs & Production w w AVC SMC MP MP and w Where is the price of the variable input A
- 14. Short-Run Production & Cost Relations
- 15. Relations Between Short-Run Costs & Production When marginal product (average product) is increasing, marginal cost (average cost) is decreasing When marginal product (average product) is decreasing, marginal cost (average variable cost) is increasing When marginal product = average product at maximum AP, marginal cost = average variable cost at minimum AVC
- 16. Isocost The combinations of inputs that cost the producer the same amount of money For given input prices, isocosts farther from the origin are associated with higher costs. Changes in input prices change the slope of the isocost line K L C1 C0 L K New Isocost Line for a decrease in the wage (price of labor).
- 17. Cost Minimization Marginal product per dollar spent should be equal for all inputs: Expressed differently r MP w MP K L r w MRTSKL
- 18. Cost Minimization Q L K Point of Cost Minimization Slope of Isocost = Slope of Isoquant
- 19. 19 The Firm’s Expansion Path An Expansion curve is formally defined as the set of combinations of capital and labor that meet the efficiency condition MPL/w = MPK/r, where w and r are wage rate and interest rate respectively. The firm can determine the cost-minimizing combinations of K and L for every level of output If input costs remain constant for all amounts of K and L the firm may demand, we can trace the locus of cost-minimizing choices called the firm’s expansion path
- 20. 20 The Firm’s Expansion Path L per period K per period q00 The expansion path is the locus of cost-minimizing tangencies q0 q1 E The curve shows how inputs increase as output increases
- 21. Equation for Expansion Path Production Function Q = 100K0.5L0.5 The marginal product functions are MPL =50 MPK = 50 Efficiency Condition is MPL/ MPK = w/r Solving for K K = (w/r).L The production function re-written as Q = 100((w/r)L)0.5 L0.5 Or Q = 100L(w/r)0.5
- 22. Example Determine the efficient input combination for producing 1000 units of output if w = 4, r = 2. Answer: 1000 = 100L(4/2)0.5 Or L = 7.07 K = (4/2) 7.07 = 14.14 The input combination ( K=14.14 and L = 7.07) is the most efficient way to produce 1000 units of output.
- 23. 23 The Firm’s Expansion Path The expansion path does not have to be a straight line the use of some inputs may increase faster than others as output expands depends on the shape of the isoquants The expansion path does not have to be upward sloping if the use of an input falls as output expands, that input is an inferior input
- 24. Revenue Total revenue – the total amount received from selling a given output TR = P x Q Average Revenue – the average amount received from selling each unit AR = TR / Q Marginal revenue – the amount received from selling one extra unit of output MR = TRn – TR n-1 units
- 25. Profit Profit = TR – TC The reward for enterprise Profits help in the process of directing resources to alternative uses in free markets Relating price to costs helps a firm to assess profitability in production
- 26. Profit Normal Profit – the minimum amount required to keep a firm in its current line of production Abnormal or Supernormal profit – profit made over and above normal profit Abnormal profit may exist in situations where firms have market power Abnormal profits may indicate the existence of welfare losses Could be taxed away without altering resource allocation
- 27. Profit Sub-normal Profit – profit below normal profit Firms may not exit the market even if sub-normal profits made if they are able to cover variable costs Cost of exit may be high Sub-normal profit may be temporary (or perceived as such!)
- 28. Profit Assumption that firms aim to maximise profit May not always hold true – there are other objectives Profit maximising output would be where MC = MR
- 29. Profit Why? Cost/Revenue Output MR MR – the addition to total revenue as a result of producing one more unit of output – the price received from selling that extra unit. MC MC – The cost of producing ONE extra unit of production 100 Assume output is at 100 units. The MC of producing the 100th unit is 20. The MR received from selling that 100th unit is 150. The firm can add the difference of the cost and the revenue received from that 100th unit to profit (130) 20 150 Total added to profit If the firm decides to produce one more unit – the 101st – the addition to total cost is now 18, the addition to total revenue is 140 – the firm will add 128 to profit. – it is worth expanding output. 101 18 140 Added to total profit 30 120 Added to total profit The process continues for each successive unit produced. Provided the MC is less than the MR it will be worth expanding output as the difference between the two is ADDED to total profit 102 40 145 104 103 Reduces total profit by this amount If the firm were to produce the 104th unit, this last unit would cost more to produce than it earns in revenue (-105) this would reduce total profit and so would not be worth producing. The profit maximising output is where MR = MC
- 30. Example A micro-entrepreneur produces caps and hats for women. The output-cost data of the business is reproduced below: Output Total Cost 50 870 100 920 150 990 200 1240 250 1440 300 1940 350 2330 a. Estimate the total cost function and then use that equation to determine the average and marginal cost functions. Assume a cost function. b. Determine the output rate that will minimize average cost and the per-unit cost at that rate of output. c. The current market price of caps and hats per unit is Tk. 9.00 and is expected to remain at that level for the foreseeable future. Should the firm continue its production?
- 31. Getting an Idea about the form of the equation 0 500 1000 1500 2000 2500 50 100 150 200 250 300 350 Output-Cost
- 32. Estimate of Example First we assume the cost function as TC = c0+c1Q + c2Q2 +c3Q3 Results TC= 954.29 -2.46Q +0.02Q2 -.0002Q3 (5.9) (-0.75) (1.04) (-0.07) R2 = 0.99 F = 197.78 Comments: t-statistics are not acceptable though R2 and F are good. Second, we assume the cost function as TC = c0+c1Q + c2Q2 Results TC = 944.29 -2.24Q + 0.02Q2 t Stat (12.51) (-2.58) (8.45) R2 = 0.99 F = 394.86 Comments: t-statistics are acceptable and R2 and F are good.
- 33. Answer to Question (a) a. The t-statistics, shown in the parenthesis of the second estimation, indicate that the coefficient of each of the independent variables are significantly different from zero. The value of the co-efficient of determination means that 99 percent of the variation in total cost is explained by changes in the rate of output.
- 34. Answer (a) contd.
- 35. Answer (b) The output rate that results in minimum per-unit cost is found by taking the first derivative of the average cost function, setting it equal to zero, and solving for Q.
- 36. Answer (b) contd. Sign mistake
- 37. Answer (c) Because the lowest possible cost is Tk. 6.45 per unit, which is above the market price of Tk. 9.00, the production should be continued.
- 38. Exercise Output Total Cost 25 700 100 920 150 990 200 1240 280 1440 360 1940 460 2330 600 3500

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