Production Analysis and Compensation Policy

1. Production Analysis and Compensation Policy Chapter 7

2. Chapter 7OVERVIEW • Production Functions • Total, Marginal, and Average Product • Law of Diminishing Returns to a Factor • Input Combination Choice • Marginal Revenue Product and Optimal Employment • Optimal Combination of Multiple Inputs • Optimal Levels of Multiple Inputs • Returns to Scale • Productivity Measurement

3. Production Functions • Properties of Production Functions • Determined by technology, equipment, and labor • Discrete functions are lumpy. • Continuous functions employ inputs in small increments. • Returns to Scale and Returns to a Factor • Returns to scale measure output effect of increasing all inputs. • Returns to a factor measure output effect of increasing one input.

4. Production Function • Total Product (TP) is whole output. • Marginal Product (MP) is the change in output caused by increasing any input X. • Average product

5. Law of Diminishing Returns • Returns to a Factor • Shows what happens to MPX as X usage grows. • MPX > 0 is common. • MPX < 0 implies irrational input use (rare). • Diminishing Returns to a Factor Concept • MPX shrinks as X usage grows, ∂2Q/∂X2 < 0. • If MPX grew with use of X, there would be no limit to input usage.

6. Total, Marginal, and AvgProduct 1 15 15 15.0 2 31 16 15.5 3 48 17 16.0 4 59 11 14.8 5 68 9 13.6 6 72 4 12.0 7 73 1 10.4 8 72 -1 9.0 9 70 -2 7.8 10 67 -3 6.7

7. Marginal Revenue Product (one input) Tractor and Wagon - A fixed resource - Production efficiency Implies Maximum Output per Worker - Perfect Competition Optimal level of a single input Hay per Hour Labor Hay Price Wage $1 $8 0 0 $1 $25 $8 1 10 10 $1 $10 $8 $1 $15 $8 2 25 15 $15 $1 $10 $8 3 50 25 $1 $5 $8 4 65 15 5 75 10 6 80 5 7 80 0

8. Multiple Input Choice All inputs are variable • Production Isoquants • Show efficient input combinations. • Technical efficiency is least-cost production. • Isoquant shape shows input substitutability. • Straight line isoquants depict perfect substitutes. • C-shaped isoquants depict imperfect substitutes. • L-shaped isoquants imply no substitutability.

9. Optimal Combination of Multiple Inputs Slope of the isoquant is Y Marginal Rate of Technical Substitution which shows amount of one input that must be substituted for another to maintain constant output Q3 Q2 Q1 X

10. Input Combination Choice Perfect Substitutes Perfect Compliments Imperfect Substitutes Gas Capital Frames C1 Q3=3 C2 Q3 Q2=2 C3 Q2 Q1=1 Q3 Q2 Q1 Q1 Wheels Diesel Labor L1 L3 L2 Where: Q1 < Q2 < Q3

11. Marginal Rate of Technical Substitution • Marginal Rate of Technical Substitution • Shows amount of one input that must be substituted for another to maintain constant output. • For inputs X and Y, MRTSXY = -MPX / MPY • Rational Limits of Input Substitution • Ridge lines show rational limits of input substitution. • MPX < 0 or MPY < 0 are never observed.

12. Marginal Rate of Technical Substitution Ridge Line Y or X Q3 Q2 Q1 Ridge Line X or Y

13. Marginal Revenue Product • Marginal Revenue Product of labor is the net revenue gain after all variable costs except labor costs. • MRPL is the maximum amount that could be paid to increase employment. • Optimal Level of a Single Input • Set MRPL=PL to get optimal employment. • If MRPL=PL, then input marginal revenue equals input marginal cost.

14. Optimal Combination of Multiple Inputs Budget Lines show how many inputs can be bought. Y Then slope of the budget line is B3 B2 B1 X

15. Optimal Combination of Multiple Inputs • Budget Lines • Show how many inputs can be bought. • Least-cost production occurs when • Expansion Path shows efficient input combinations as output grows. • Illustration of Optimal Input Proportions • Input proportions are optimal when no additional output could be produce for the same cost. • Optimal input proportions is a necessary but not sufficient condition for profit maximization. or

16. Optimal Combination of Multiple Inputs Optimal when Y B3 expansion path Equilibrium (minimum cost output) when the slope of the budget line is equal to the isoquant slope B2 Y3 Q3 Y2 B1 When Y1 Q2 Q1 X1 X2 X3 X

17. Optimal Combination of Multiple Inputs The Tax Advisors, Inc. currently has three CPAs and four bookkeepers. Bookkeeper wages are $30 per hour and have MP=0.3. CPAs currently receive hourly pay of $70 per hour with MP=1.4. The Tax Advisors, Inc. should increase use of CPAs which will decrease their MP and also reduce use of bookkeepers thus increasing their MP

18. Optimal Combination of Multiple Inputs The numbers may also be used to calculate MC of production using alternative labor sources (bookkeepers vs. CPAs). The CPAs have lowest MC as the moment thus hire a CPA next.

19. Education Example MPta MPct MPsp MPad ta – teacher aid ct – certified teacher sp – Specialist ad – Administrator = = = Pta Pct Psp Pad Pta = $15,000 Pct = $30,000 Psp = $35,000 Pad = $50,000 MPta= 30,000 MPct= 70,000 MPsp= 70,000 MPad= 90,000 Aid Certified Specialist Administrator 30,000 70,000 70,000 90,000 $50,000 $15,000 $30,000 $35,000 2.33 2 2 1.8 The next person hired should be a: Certified Teacher

20. Optimal Levels of Multiple Inputs • Optimal Employment and Profit Maximization • Profits are maximized when MRPX = PX for all inputs. • Profit maximization requires optimal input proportions plus an optimal level of output. • Profit maximization means efficiently producing what customers want.

21. Returns to Scale • Returns to scale show the output effect of increasing all inputs. • Output elasticity is εQ = ∂Q/Q ÷ ∂Xi/Xi where Xi is all inputs (labor, capital, etc.) • Output Elasticity and Returns to Scale • εQ > 1 implies increasing returns. • εQ = 1 implies constant returns. • εQ < 1 implies decreasing returns.

22. Returns to Scale Total Product (Q) Increasing Returns Constant Returns Decreasing Returns Units of X and Y

23. Productivity Measurement • Economic Productivity • Productivity growth is the rate of change in output per unit of input. • Labor productivity is the change in output per worker hour. • Causes of Productivity Growth • Efficiency gains reflect better input use. • Capital deepening is growth in the amount of capital workers have available for use.

24. Example (Labor Productivity) Assume an isoquant Suppose K is fixed at 16 units short run assumption What is production when labor is 100 What is the marginal productivity of labor

25. Example (Labor Productivity) When labor is 40, MP is Again if this market is perfectly competitive MR=P Suppose the product price is $40 If wage rate is $10, would you use the 40th worker?

26. Example (Advertising) TV ads cost $400 each, radio ads $300 each You have an advertising budget of $2,000 The marginal value of running additional ads are list below Marginal Productivity (Gross Rating Points) Marginal Productivity per dollar spend Radio $300 $700 TV $400 $1,000 Radio $300 $1,300 Radio $300 $1,600 Radio $300 $2,000 TV $400 Purchase two TV spots and four Radio Spots

27. Example (Appliances) A manufacturer of home appliances faces the production function and input cost of PL = $10 and PK=$15. If K = 8 and L = 10, then Minimum cost of producing 636 units