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Multiple Input Cost Relationships

Multiple Input Cost Relationships. Isoquant means “equal quantity”. Output is identical along an isoquant. Two inputs. Page 104 in booklet. Slope of an Isoquant. The slope of an isoquant is referred to as the Marginal Rate of Technical Substitution, or

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Multiple Input Cost Relationships

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  1. Multiple Input Cost Relationships

  2. Isoquant means “equal quantity” Output is identical along an isoquant Two inputs Page 104 in booklet

  3. Slope of an Isoquant The slope of an isoquant is referred to as the Marginal Rate of Technical Substitution, or MRTS. The value of the MRTS in our example is given by: MRTS = Capital ÷ labor If output remains unchanged along an isoquant, the loss in output from decreasing labor must be identical to the gain in output from adding capital.

  4. Plotting the Iso-Cost Line Firm can afford 10 units of capital at a rental rate of $100 for a budget of $1,000 Capital 10 Firm can afford 100 units of labor at a wage rate of $10 for a budget of $1,000 Labor 100

  5. Slope of an Iso-cost Line The slope of an iso-cost in our example is given by: Slope = - (wage rate÷ rental rate) or the negative of the ratio of the price of the two Inputs. The slope is based upon the budget constraint and can be obtained from the following equation: ($10×use of labor)+($100×use of capital)

  6. Least Cost Decision Rule The least cost combination of two inputs (labor and capital in our example) occurs where the slope of the iso-cost line is tangent to isoquant: MPPLABOR÷ MPPCAPITAL= -(wage rate÷ rental rate) Slope of an isoquant Slope of iso- cost line

  7. Least Cost Decision Rule The least cost combination of labor and capital in out example also occurs where: MPPLABOR÷ wage rate = MPPCAPITAL÷ rental rate MPP per dollar spent on labor MPP per dollar spent on capital =

  8. Least Cost Decision Rule This decision rule holds for a larger number of inputs as well… The least cost combination of labor and capital in out example also occurs where: MPPLABOR÷ wage rate = MPPCAPITAL÷ rental rate MPP per dollar spent on labor MPP per dollar spent on capital =

  9. Least Cost Input Choice for 100 Units At the point of tangency, we know that: slope of isoquant = slope of iso-cost line, or… MPPLABOR÷ MPPCAPITAL = - (wage rate÷ rental rate) Page 104 in booklet

  10. What Inputs to Use for a Specific Budget? Firm can afford to produce only 75 units of output using C3 units of capital and L3 units of labor Page 104 in booklet

  11. The Planning Curve The long run average cost (LAC) curve reflects points of tangency with a series of short run average total cost (SAC) curves. The point on the LAC where the following holds is the long run equilibrium position (QLR) of the firm: SAC = LAC = PLR where MC represents marginal cost and PLR represents the long run price, respectively.

  12. What can we say about the four firm sizes in this graph? Page 102 in booklet

  13. Size 1 would lose money at price P Page 102 in booklet

  14. Firm size 2, 3 and 4 would earn a profit at price P…. Q3 Page 102 in booklet

  15. Firm size #2’s profit would be the area shown below… Q3 Page 102 in booklet

  16. Firm size #3’s profit would be the area shown below… Q3 Page 102 in booklet

  17. Firm size #4’s profit would be the area shown below… Q3 Page 102 in booklet

  18. If price were to fall to PLR, only size 3 would not lose money; it would break-even. Size 4 would have to down size its operations! Page 102 in booklet

  19. How to Expand Firm’s Capacity Optimal input combination for output=10 Page 107 in booklet

  20. How to Expand Firm’s Capacity Two options: 1. Point B ? Page 107 in booklet

  21. How to Expand Firm’s Capacity Two options: 1. Point B? 2. Point C? Page 107 in booklet

  22. Expanding Firm’s Capacity Page 107 in booklet

  23. Expanding Firm’s Capacity This combination costs more to produce 20 units of output since budget HI exceeds budget FG Page 107 in booklet

  24. Expanding Firm’s Capacity Optimal input combination for output=20 with budget FG Optimal input combination for output=10 with budget DE Page 107 in booklet

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