Managerial Economics in a Global Economy

1. Managerial Economicsin a Global Economy Chapter 6 Production Theory and Estimation

2. The production function with one variable • Inputs • Labor, Capital, Land …etc. • Fixed Inputs • Variable Inputs • Short Run • At least one input is fixed • Long Run • All inputs are variable

3. TPL MPL = TPL APL= • Total Product TP = Q = f(L) • Average Product The total product divided by the amount of the input used. • Marginal Product The addition to total output resulting from the addition of the last unit of the input. - Marginal product = negative when TP is decreasing - Marginal product = zero when TP is at its maximum - Marginal output = Average product when AP reaches maximum

4. MPLAPL EL = • Production or Output Elasticity The production function is a table, graph, or an equation showing the maximum output from inputs. The following table is an example (where there is one variable input, the remaining are constant).

6. The Law of Diminishing Returns. If equal increments of an input are added, and the quantities of other inputs are held constant, the resulting increments of product will decrease beyond some point; that is, the marginal product of the input will diminish. Note: - The law is an empirical generalization - Technology is assumed to be constant - There is a change in one input and the others are held constant

7. Stages of Production

8. The Optimal Level of Utilization of an Input. • How much of the variable input should we utilize?. The answer: we have to compare between the marginal revenue product MRPof the input and themarginal expenditure on the input i.e., the marginal resource cost MRC. • The Marginal Revenue Product: The amount that an additional unit of the variable input (Y) adds to the firm’s total revenue: MRPL = (TR/Q) . (Q/L) (marginal revenue × marginal product), Or: MRPL = MR . MPL

9. The Marginal Resource Cost • The amount that an additional unit of the variable input adds to the firms total costs. MRCL = TC/L; (wage level in a competitive labor market) • To maximize its profits, the firm should utilize the amount of input where the marginal revenue product equals the marginal expenditures. Optimal Use of Labor  MRPL = MRCL

10. Optimal Use of the Variable Input Look at the table. The use of Labor is Optimal When L = 3.50

11. Optimal Use of the Variable Input

12. The Production Function with Two Variable Inputs. Q = f ( X1 , X2 ); • production function Capital 6 10 21 31 3640 39 5 12283640 42 40 4 122836404036 3 10 23 23 3636 33 2 7 18 28 30 30 28 1 3 8 12 14 14 12 1 2 3 4 5 6 Labor

13. Isoquants • A curve showing all possible (efficient) combinations of (two) inputs that are capable of producing a certain quantity of output Production With Two Variable Inputs

14. Isoquants slope is negative, but it may also have positively sloped segments. Positive slope implies that increases in both capital and labor are required to maintain a certain output rate. In this case the marginal product of one or the other input must be negative. • Economic Region of Production • Firms will only use combinations of two inputs that are in the economic region of production, which is defined by the portion of each isoquant that is negatively sloped.

15. Hence output will increase if less quantities of the input were used. profit maximizing firms will produce on the negatively slopped curves only.

16. Marginal Rate of Technical Substitution MRTS • The rate at which an input can be substituted for another input if output remains constant Q = f ( X1 , X2 ) • MRTS = - dX2 / dX1; the slope of the isoquant • Since MRTS = - dX2 / dX1, it follows that (given capital and labor are the two inputs) • MRTS = -K/L = MPL/MPK

17. MRTS = -(-2.5/1) = 2.5

18. Perfect SubstitutesPerfect Complements

19. Optimal Combination of Inputs • Input combinations that can be obtained from a total outlay M is: M =PL . L + PK . K; • The various combinations of capital and labor can be represented by a straight line. This line is called the isocost curve. Its slope is: -PL / PK. • Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost. C = total cost W = wage rate r = cost of capital

20. Isocost Lines • AB C = $100, w = r = $10 • A’B’ C = $140, w = r = $10 • A’’B’’ C = $80, w = r = $10 • AB* C = $100, w = $5, r = $10

21. To determine the optimal combination of inputs, we superimpose the isocost on the isoquant map.

22. The firm should pick the point on the isocost that is on (tangent) the highest isoquant. i.e, MPL / MPK = PL / PK • Or MPL / PL = MPK / PK ( maximization condition ) • If we use more than two inputs the optimal combination of inputs is: MPa / Pa = MPb / Pb = . . . = MPn / Pn

23. Effect of a Change in Input Prices

24. Returns to Scale • How output responds in the long run to changes in the scale of the firm. Suppose that the firm increases inputs by the same proportion; what will happen to output. a - output may increase by a larger proportion of each input. This is the case of increasing returns to scale. b - output may increase by a smaller proportion than each of the inputs. This is the case of decreasing returns to scale. c - output may increase by the same proportion of each of the inputs. This is the case of constant returns to scale.

25. Production Function Q = f (L, K) Q = f (hL, hK) • If  = h, then f has constant returns to scale. • If  > h, then f has increasing returns to scale. • If  < h, the f has decreasing returns to scale. Constant Returns Increasing Decreasing Returns to Scale Returns to Scale to Scale

26. Causes of increasing returns to scale. - geometric relations (technical characteristics of tools) - specialization - probabilistic considerations, the greater the number of customers, customer behavior tends to be more stable, the firm’s inventory may not need to increase in proportion to its sales • Causes of decreasing returns to scale - the difficulty of coordinating a large scale enterprise. large teams seem to be less effective than small teams

27. The output elasticity ε • To measure whether there are increasing or decreasing returns or constant returns to scale, the output elasticity can be computed. • The output elasticity is the percentage change in output resulting from one percentage change in all inputs. • If ε > 1  increasing returns to scale • If ε < 1  decreasing returns to scale • If ε = 1  constant returns to scale

28. Cobb-Douglas Production Function Q = AKaLb • Estimated using Natural Logarithms ln Q = ln A + a ln K + b ln L • If a+b = 1 constant returns • If a+b > 1 increasing returns • If a+b < 1 decreasing returns

29. Innovations and Global Competitiveness • Product Innovation • Process Innovation • Product Cycle Model • Just-In-Time Production System • Competitive Benchmarking • Computer-Aided Design (CAD) • Computer-Aided Manufacturing (CAM)

33. e.g. Q = 0.8L0.3 K0.8 multiply both inputs by 1.01 Q = 0.8(1.01L).3 ( 1.01K).8 = 0.8(1.01)1.1L.3K.8 = (1.01)1.1 (.8L.3 K.8) = (1.01)1.1 Q = 1.011 Q • if the quantity of both inputs increases by 1% output will increase by 1.1%.