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Economics of Input and Product Substitution

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1. Topics of Discussion • Concepts of isoquants and iso-cost line • Least-cost use of inputs • Long-run expansion of input use • Economics of business expansion and contraction • Production possibilities frontier • Profit maximizing combination of products

2. Physical Relationships

3. Isoquant means “equal quantity” Output is identical along an isoquant Two inputs Page 133

4. 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 Page 133

5. 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. Page 133

6. MRTS here is -4÷1= -4 Page 133

7. What is the slope over range B? Page 133

8. What is the slope over range B? MRTS here is -1÷1= -1 Page 133

9. What is the slope over range C? Page 133

10. What is the slope over range C? MRTS here is -.5÷1= -.5 Page 133

11. Introducing Input Prices

12. 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 Labor 100 Page 136

13. 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 Page 136

14. 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. See footnote 5 on page 179 for the derivation of this slope based upon the budget constraint (hint: solve equation below for the use of capital). (\$10×use of labor)+(\$100×use of capital)=\$1,000 Page 135

15. Original iso-cost line Change in budget or both costs Line AB represents the original iso-cost line for capital and labor… Change in wage rate Change in rental rate Page 136

16. Original iso-cost line Change in budget or both costs The iso-cost line would shift out to line EF if the firm’s available budget doubled (or costs fell in half) or back to line CD if the available budget halved (or costs doubled. Change in wage rate Change in rental rate Page 136

17. Original iso-cost line Change in budget or both costs Change in wage rate Change in rental rate If wage rates fell in half, the line would shift out to AF. The iso-cost line would shift in to line AD if wage rates doubled… Page 136

18. Original iso-cost line Change in budget or both costs Change in wage rate Change in rental rate The iso-cost line would shift out to line BE if rental rate fell in half while the line would shift in to line BC if the rental rate for capital doubled… Page 136

19. Least Cost Combinationof Inputs

20. 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 list is tangent to the isoquant: MPPLABOR÷ MPPCAPITAL= -(wage rate÷ rental rate) Slope of an isoquant Slope of iso- cost line Page 139

21. 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 = Page 139

22. 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 = Page 139

23. Least Cost Input Choice for 100 Units Iso-cost line for \$1,000. Its slope reflects price of labor and capital. Page 138

24. Least Cost Input Choice for 100 Units We can determine this graphically by observing where these two curves are tangent…. Page 138

25. Least Cost Input Choice for 100 Units We can shift the original iso-cost line from AB out in a parallel fashion to A*B* (which leaves prices unchanged) which just touches the isoquant at G Page 138

26. 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 138

27. Least Cost Input Choice for 100 Units At the point of tangency, therefore, the MPP per dollar spent on labor is equal to the MPP per dollar spent on capital!!! See equation (8.5) on page 181, which is analogous to equation (4.2) back on page 76 for consumers. Page 138

28. Least Cost Input Choice for 100 Units This therefore represents the cheapest combination of capital and labor to produce 100 units of output… Page 138

29. Least Cost Input Choice for 100 Units If I told you the value of C1 and L1 and asked you for the value of A* and B*, how would you find them? Page 138

30. Least Cost Input Choice for 100 Units If I told you that point G represents 7 units of capital and 60 units of labor, and that the wage rate is \$10 and the rental rate is \$100, then at point G we must be spending \$1,300, or: \$100×7+\$10×60=\$1,300 7 60 Page 138

31. Least Cost Input Choice for 100 Units If point G represents a total cost of \$1,300, we know that every point on this iso-cost line also represents \$1,300. If the wage rate is \$10, then point B* must represent 130 units of labor, or: \$1,300\$10 = 130 7 130 60 Page 138

32. Least Cost Input Choice for 100 Units And the rental rate is \$100, then point A* must represents 13 units of capital, or: \$1,300 \$100 = 13 13 7 130 60 Page 138

33. What Happens if the Price of an Input Changes?

34. What Happens if Wage Rate Declines? Assume the initial wage rate and cost of capital results in the iso-cost line AB Page 140

35. What Happens if Wage Rate Declines? Wage rate decline means that the firm can now afford B* instead of B… Page 140

36. What Happens if Wage Rate Declines? The new point of tangency occurs at H rather than G. Page 140

37. What Happens if Wage Rate Declines? As a consequence, the firm would desire to use more labor and less capital… Page 140

38. What Inputs to Use for a Specific Budget? M An iso-cost line for a specific budget Capital N Labor Page 141

39. What Inputs to Use for a Specific Budget? A set of isoquants for different levels of output… Page 141

40. 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 141

41. What Inputs to Use for a Specific Budget? The firm’s budget is not large enough to operate at 100 or 125 units… Page 141

42. What Inputs to Use for a Specific Budget? Firm is not spending available budget here… Page 141