Chapter 7. The Cost of Production. ΔVC Δq. ΔTC Δq. Fixed and Variable Costs. Fixed Cost Versus Sunk Cost. Measuring Costs
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1 Chapter 7 The Cost of Production Fixed and Variable Costs Total output is a function of variable inputs and fixed inputs. Therefore, the total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or TC FC VC 2005 Pearson Education, Inc. Chapter 7 2 Fixed Cost Versus Sunk Cost Fixed cost and sunk cost are often confused Fixed Cost Cost paid by a firm that is in business regardless of the level of output Sunk Cost Cost that have been incurred and cannot be recovered Measuring Costs Marginal Cost (MC): MC ΔTC Δq ΔVC Δq 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 4
2 Cost ($/unit) Measuring Costs Firm s Short Run Costs verage Total Cost (TC) TC TC q TFC TVC q q TC TC FC q VC 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 6 Cost ($ per year) Cost Curves for a Firm Total cost is the vertical sum of FC and VC Pearson Education, Inc. Chapter 7 7 TC VC Variable cost increases with production and the rate varies with increasing & decreasing returns. Fixed cost does not vary with output FC Output Cost Curves MC TC VC 20 0 FC Output (units/yr) Pearson Inc. Chapter Education, 8
3 Cost Curves Cost Curves for a Firm When MC is below VC, VC is falling When MC is above VC, VC is rising When MC is below TC, TC is falling When MC is above TC, TC is rising Therefore, MC crosses VC and TC at the minimums The line drawn from the origin to the variable cost curve: Its slope equals VC The slope of a point on VC or TC equals MC Therefore, MC = VC at 7 units of output (point ) P TC VC FC Output 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 10 Capital is either rented/leased or purchased ssume Delta is considering purchasing an airplane for $150 million Plane lasts for 30 years $5 million per year economic depreciation for the plane If the firm had not purchased the plane, it would have earned interest on the $150 million Forgone interest is an opportunity cost that must be considered 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 12
4 User Cost of Capital = Economic Depreciation + (Interest Rate)*(Value of Capital) = $5 mil + (.10)($150 mil depreciation) Year 1 = $5 million + (.10)($150 million) = $20 million Year 10 = $5 million +(.10)($100 million) = $15 million User cost can also be described as; Rate per dollar of capital, r r = Depreciation Rate + Interest Rate In our example, depreciation rate was 3.33% and interest was 10% so r = 3.33% + 10% = 13.33% 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 14 The Isocost Line line showing all combinations of L & K that can be purchased for the same cost Total cost of production is sum of firm s labor cost, wl and its capital cost rk C = wl + rk Rewriting C as an equation for a straight line: K = C/r - (w/r)l Slope of the isocost: K w L r 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 16
5 Producing a Given Output at Minimum Cost Capital per year K 2 K 1 K 3 Q 1 is an isoquant for output Q 1. There are three isocost lines, of which 2 are possible choices in which to produce Q1 Isocost C 2 shows quantity Q 1 can be produced with combination K 2 L 2 or K 3 L 3. However, both of these are higher cost combinations than K 1 L 1. Q 1 Input Substitution When an Input Price Change If the price of labor changes, then the slope of the isocost line change, w/r It now takes a new quantity of labor and capital to produce the output If price of labor increases relative to price of capital, and capital is substituted for labor L 2 L 1 C 0 C 1 C 2 L 3 Labor per year 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 18 Input Substitution When an Input Price Change Capital per year If the price of labor rises, the isocost curve becomes steeper due to the change in the slope -(w/l). How does the isocost line relate to the firm s production process? K 2 K 1 B The new combination of K and L is used to produce Q 1. Combination B is used in place of combination. MRTS - K MPL L MPK Slope of isocost line K w L r C 2 C 1 Q 1 MPL w MP r K when firmminimizes cost L 2 L 1 Labor per year 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 20
6 Cost minimization with Varying Output Levels firm s expansion path shows the minimum cost combinations of labor and capital at each level of output. Slope equals K/L 2005 Pearson Education, Inc. Chapter 7 21 Firm s Expansion Path Capital per year 150 $ $ B C 200 Units The expansion path illustrates the least-cost combinations of labor and capital that can be used to produce each level of output in the long-run. Expansion Path 300 Units Labor per year 2005 Pearson Education, Inc. Chapter 7 22 Expansion Path & Long-run Costs Firm s Long-Run Total Cost Curve Firms expansion path has same information as long-run total cost curve To move from expansion path to LR cost curve Find tangency with isoquant and isocost Determine min cost of producing the output level selected Graph output-cost combination Cost/ Year D E F Long Run Total Cost Output, Units/yr 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 24
7 Short-Run vs. Long-Run Long-Run verage and Marginal Cost Capital per year E C K 2 Capital is fixed at K1 To produce q1, min cost at K1,L1 If increase output to Q2, min cost is K1 and L3 in short run Long-Run Expansion Path P Short-Run Expansion Path In LR, can change capital and min costs falls to K2 and L2 Cost ($ per unit of output LMC LC K 1 Q 2 Q 1 L 1 L 2 B L 3 D F Labor per year Output 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 26 Economies and Diseconomies of Scale Economies of Scale Increase in output is greater than the increase in inputs. Diseconomies of Scale Increase in output is less than the increase in inputs. U-shaped LC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels Long Run Costs Increasing Returns to Scale Output more than doubles when the quantities of all inputs are doubled Economies of Scale Doubling of output requires less than a doubling of cost 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 28
8 Long-Run Cost with Economies and Diseconomies of Scale Many firms produce more than one product and those product are closely linked Examples: Chicken farm--poultry and eggs utomobile company--cars and trucks University--Teaching and research 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 30 dvantages 1. Both use capital and labor. 2. The firms share management resources. 3. Both use the same labor skills and type of machinery. The alternative quantities can be illustrated using product transformation curves Curves showing the various combinations of two different outputs (products) that can be produced with a given set of inputs 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 32
9 Product Transformation Curve Product Transformation Curve Number of tractors O 1 Each curve shows combinations of output with a given combination of L & K. O 2 O 1 illustrates a low level of output. O 2 illustrates a higher level of output with two times as much labor and capital. Product transformation curves are negatively slope To get more of one output, must give up some of the other output Curve is concave Joint production has its advantages Number of cars 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 34 There is no direct relationship between economies of scope and economies of scale. May experience economies of scope and diseconomies of scale May have economies of scale and not have economies of scope The degree of economies of scope (SC) can be measured by percentage of cost saved producing two or more products jointly: SC C(q1 ) C(q2 ) C(q1, q2 ) C(q1, q2 ) C(q 1 ) is the cost of producing q 1 C(q 2 ) is the cost of producing q 2 C(q 1,q 2 ) is the joint cost of producing both products 2005 Pearson Education, Inc. Chapter Pearson Education, Inc. Chapter 7 36
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