1. Production Costs ECO61 Udayan Roy Fall 2008

2. Bundles of Labor and Capital That Cost the Firm $100

3. Isocost Lines K, Units of capital per y ear a d e $100 isocost L, Units of labor peryear $100 $10 10 = $100 $5 = 20 Isocost Equation K = r - L w r C Initial Values C = $100 w = $5 r = $10 15 2.5 10 5 7.5 5 c b  L = 5  K = 2.5 For each extra unit of capital it uses, the firm must use two fewer units of labor to hold its cost constant. Slope = -1/2 = - w/r

4. A Family of Isocost Lines K, Units of capital per y ear a e $150 isocost$100 isocost L, Units of labor peryear $150 $10 15 = $100 $10 10 = $100 $5 = 20 $150 $5 = 30 Isocost Equation K = r - L w r C Initial Values C = $150 w = $5 r = $10 An increase in C….

5. A Family of Isocost Lines K, Units of capital per y ear a e $150 isocost$100 isocost$50 isocost L, Units of labor peryear $150 $10 15 = $100 $10 10 = $50 $10 5 = $50 $5 = 10 $100 $5 = 20 $150 $5 = 30 Isocost Equation K = r - L w r C Initial Values C = $50 w = $5 r = $10 A decrease in C….

6. Costs The firm’s total cost equation is: C = wL + rK. – Therefore, Note that if C is constant—as along an isocost line—then a one-unit increase in L requires K to change by –w/r units. That is, the slope of the isocost line is –w/r.

7. Combining Cost and Production Information. The firm can choose any of three equivalent approaches to minimize its cost: – Lowest-isocost rule - pick the bundle of inputs where the lowest isocost line touches the isoquant. – Tangency rule - pick the bundle of inputs where the isoquant is tangent to the isocost line. – Last-dollar rule - pick the bundle of inputs where the last dollar spent on one input gives as much extra output as the last dollar spent on any other input.

8. Cost Minimization K, Units of capital per hour x 500 L, Units of labor per hour 100 q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost Isocost Equation K = r - L w r C Initial Values q = 100 C = $2,000 w = $24 r = $8 Isoquant Slope MP L MP K =-MRTS - Which of these three Isocost would allow the firm to produce the 100 units of output at the lowest possible cost?

9. Cost Minimization K, Units of capital per hour y x z 11650240 L, Units of labor per hour 100 303 28 q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost Isocost Equation K = r - L w r C Initial Values q = 100 C = $2,000 w = $24 r = $8 Isoquant Slope MP L MP K =MRTS -

10. Cost Minimization At the point of tangency, the slope of the isoquant equals the slope of the isocost. Therefore, last-dollar rule: cost is minimized if inputs are chosen so that the last dollar spent on labor adds as much extra output as the last dollar spent on capital. Slope of isoquant Slope of isocost

11. Cost Minimization K, Units of capital per hour y x z 11650240 L, Units of labor per hour 100 303 28 q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost Initial Values q = 100 C = $2,000 w = $24 r = $8 w r MP L MP K = MP L = 0.6q/L MP K = 0.4q/K = 248 1.2 0.4 = = 0.05 Spending one more dollar on labor at x gets the firm as much extra output as spending the same amount on capital.

12. Cost Minimization K, Units of capital per hour y x z 11650240 L, Units of labor per hour 100 303 28 q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost Initial Values q = 100 C = $2,000 w = $24 r = $8 w r MP L MP K MP L = 0.6q/L MP K = 0.4q/K = 24 8 2.5 0.13 = = 0.1 if the firm shifts one dollar from capital to labor, output falls by 0.017 because there is less capital but also increases by 0.1 because there is more labor for a net gain of 0.083 more output at the same cost…. = 0.02 So …the firm should shift even more resources from capital to labor—which increases the marginal product of capital and decreases the marginal product of labor.

13. Change in Input Price K, Units of capital per hour x 77500L,Workers per hour 100 52 q = 100 isoquant Original isocost, $2,000 New isocost, $1,032 w r MP L MP K = Minimizing Cost Rule A decrease in w…. Initial Values q = 100 C = $2,000 w = $24 r = $8 w 2 = $8 C 2 = $1,032 v

14. How Long-Run Cost Varies with Output expansion path - the cost-minimizing combination of labor and capital for each output level

15. Expansion Path K, Units of capital per hour x y z 10075500L,Workers per hour 150 200 100 Expansion path $3,000 isocost $2,000 isocost $4,000 isocost q = 100 Isoquant q = 200 Isoquant q = 300 Isoquant

16. Expansion Path and Long-Run Cost Curve (cont’d)

17. Long-Run Cost Curves

18. Economies of Scale economies of scale - property of a cost function whereby the average cost of production falls as output expands. diseconomies of scale - property of a cost function whereby the average cost of production rises when output increases.

19. Returns to Scale and Long-Run Costs

20. Figure 8.7: Least-Cost Method, No-Overlap Rule Example Q = 140 Square Feet of Space, K 123456 500 1000 1500 2000 2500 Number of Assembly Workers, L B A C = $3500 D C = $3000 8-20

21. Figure 8.10: Output Expansion Path and Total Cost Curve 8-21

22. Figure 8.28: Returns to Scale and Economies of Scale 8-22