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… Chapter 7 11

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 Chapter 7 12

Measuring Costs Marginal Cost (MC): Chapter 7 14

Measuring Costs Average Total Cost (ATC) Chapter 7 15

A Firm’s Short Run Costs Chapter 7

Cost Curves for a Firm TC VC Cost 400 300 200 100 FC 50 Output 1 2 3 4 ($ per year) 100 200 300 400 1 2 3 4 5 6 7 8 9 10 11 12 13 VC Total cost is the vertical sum of FC and VC. Variable cost increases with production and the rate varies with increasing & decreasing returns. Fixed cost does not vary with output FC 50 Chapter 7 33

Cost Curves MC ATC AVC AFC Chapter 7

Cost Curves When MC is below AVC, AVC is falling When MC is above AVC, AVC is rising When MC is below ATC, ATC is falling When MC is above ATC, ATC is rising Therefore, MC crosses AVC and ATC at the minimums Chapter 7

Cost Curves for a Firm The line drawn from the origin to the variable cost curve: Its slope equals AVC The slope of a point on VC or TC equals MC Therefore, MC = AVC at 7 units of output (point A) 1 2 3 4 5 6 7 8 9 10 11 12 13 Output P 100 200 300 400 FC VC TC A Chapter 7 39

Cost in the Long Run Capital is either rented/leased or purchased Assume Delta is considering purchasing an airplane for $150 million Plane lasts for 30 years $5 million per year – economic depreciation for the plane Chapter 7

Cost in the Long Run 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 Chapter 7 43

Cost in the Long Run 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 Chapter 7 43

Cost in the Long Run 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% Chapter 7 43

Cost in the Long Run The Isocost Line C = wL + rK A 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 Chapter 7 44

Cost in the Long Run Rewriting C as an equation for a straight line: K = C/r - (w/r)L Slope of the isocost: Chapter 7 45

Producing a Given Output at Minimum Cost Capital per year Q1 is an isoquant for output Q1. There are three isocost lines, of which 2 are possible choices in which to produce Q1 C2 Q1 A K1 L1 K3 L3 K2 L2 C1 Isocost C2 shows quantity Q1 can be produced with combination K2L2 or K3L3. However, both of these are higher cost combinations than K1L1. C0 Labor per year Chapter 7 52

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 Chapter 7

Input Substitution When an Input Price Change Capital per year C2 If the price of labor rises, the isocost curve becomes steeper due to the change in the slope -(w/L). Q1 C1 The new combination of K and L is used to produce Q1. Combination B is used in place of combination A. K2 L2 B K1 L1 A Chapter 7 Labor per year 55

Cost in the Long Run How does the isocost line relate to the firm’s production process? Chapter 7 56

Cost in the Long Run Cost minimization with Varying Output Levels A firm’s expansion path shows the minimum cost combinations of labor and capital at each level of output. Slope equals K/L Chapter 7 65

A Firm’s Expansion Path Capital per year 25 50 75 100 150 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. $3000 300 Units C Expansion Path $2000 200 Units B A Labor per year 100 150 300 200 50 Chapter 7 72

Expansion Path & Long-run Costs 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 Chapter 7

A Firm’s Long-Run Total Cost Curve Cost/ Year 1000 2000 3000 Long Run Total Cost D E F Output, Units/yr 100 300 200 Chapter 7 72

To produce q1, min cost at K1,L1 If increase output to Q2, min cost Short-Run vs. Long-Run Capital per year F E L2 Q2 K2 D C 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 Q1 A B L1 K1 Long-Run Expansion Path In LR, can change capital and min costs falls to K2 and L2 L3 P Short-Run Expansion Path Labor per year Chapter 7 77

Long-Run Average and Marginal Cost ($ per unit of output LMC A LAC Output Chapter 7 85

Economies and Diseconomies 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 LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels Chapter 7 87

Long Run Costs Increasing Returns to Scale Economies of 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 Chapter 7

Long-Run Cost with Economies and Diseconomies of Scale Chapter 7 102

Production with Two Outputs – Economies of Scope Many firms produce more than one product and those product are closely linked Examples: Chicken farm--poultry and eggs Automobile company--cars and trucks University--Teaching and research Chapter 7 105

Production with Two Outputs – Economies of Scope Advantages Both use capital and labor. The firms share management resources. Both use the same labor skills and type of machinery. Chapter 7 107

Production with Two Outputs – Economies of Scope 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 Chapter 7 108

Product Transformation Curve Number of tractors Each curve shows combinations of output with a given combination of L & K. O2 O1 illustrates a low level of output. O2 illustrates a higher level of output with two times as much labor and capital. O1 Number of cars Chapter 7 111

Product Transformation Curve 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 Chapter 7 112

Production with Two Outputs – Economies of Scope 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 Chapter 7 113

Production with Two Outputs – Economies of Scope The degree of economies of scope (SC) can be measured by percentage of cost saved producing two or more products jointly: C(q1) is the cost of producing q1 C(q2) is the cost of producing q2 C(q1,q2) is the joint cost of producing both products Chapter 7 114