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- QUESTION 39 The folllowing table shows data for a simple production function. Capital (K). Labor (L) 10 0 10 1 10 2 3 4 5 6 10 10 10 10 TP or Q AP MP 6 14 20 14 8 Assume that the cost of capital, PK, is $50 per unit, and the cost of labor, PL, is $100 per unit. Marginal cost, MC, is at minimum when labor, L, is equal to O2 units. O4 units. O 3 units. 5 units.8. If a firm has a production function of the form: Q = L0.5K2, what can we conclude? (a) The firm has a quasi-concave production function and will experience constant marginal returns to labour and increasing marginal returns to capital. (b) The firm has a quasi-concave production function and will experience decreasing marginal returns to labour and increasing marginal returns to capital. (c) The firm has a convex production function and will experience increasing marginal returns to labour and increasing marginal returns to capital. (d) The firm has a convex production function and will experience constant marginal returns to labour and increasing marginal returns to capital. (e) The firm has a linear production function and will experience decreasing marginal returns to labour and increasing marginal returns to capital.5. A company that produces auto parts has a production function of Q = 300 L-75 K-5. %3D If L= 250 and K= 25, what is the output of auto parts? If L increases to 350, what is the output of auto parts? What does the change in output show regarding labor as a factor of production?
- Which of the following production functions exhibits increasing returns to scale in the factors of production K and L? a. y = ĀK0.3 L0.75 b. y = Kª(ĀL)-e,0 < a < 1 c. y = ĀKO.3L0.3 d. y = ĀK/4 + L³/46. Which one of the following production functions represents an increasing returns to scale technology, where e is labour and k is capital? a) F(£,k) = e1/2 + k1/2. b) G(2,k) = {2/3k^/2. c) H(e,k) = min{{, 2k} d) I(e, k) = 3l + 2k.Q. Table 3 above shows how output varies with only one variable input used in production. If the cost of a unit of labor is $500, what is the approximate marginal cost of the 230th unit of output? a. $2.50 b. $8.50 c. $12.50 d. $50.00 e. $100.00
- oj Consider the Cobb-Douglas production function P(L, K) = 6L0.6 K04_ Find the %3D total units of production when 19 units of labor and 12 units of capital are invested.The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C)=²1C²2 where co. ₁, and care constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume co5, c, 0.25, and c₂-0.75. Assume sach unit of labor costs $25 and each unit of capital costs $75. With $70,000 available in the budget, devalop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. Max s.t. L, CZO € 70,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0S LS 3,000 and 0 s Cs 1,000. Round your answers to the nearest integer when necessary.) units at (L. C)=(Suppose the representative firm of the economy has a production function of the form F(K, N) = AKO.5N 0.5 The marginal product of labor is then given by MP N = 0.5AK0.5N –0.5 . The current capital 3. stock is K = 40. (a) Holding fixed capital at 40, draw a graph of output as a function of labor. What are some important features of this graph? (b) If A = 4 what is the Labor Demand Curve, ND(w), as a function of the real wage w? (c) Suppose labor is supplied inelastically with NS(w)= 10. What is the equilibrium wage w, employment level N, and full employment output Y ? (d) Suppose that productivity unexpectedly increases to A = 6. What is the new equilibrium wage w, employment level N, and full employment output Y ? (e) Depict this change graphically. Denote the original labor supply and demand curves by NS and ND respectively. Denote the new labor demand curve after the productivity shock by ND' . (Does not need to be to scale).
- Question parts b2, b3, b410. An isoprofit curve will have which of the following properties? (a) If an extra unit of capital is used, output will rise by AQ = MP₁AL (b) If an extra unit of capital is used, the value of the extra output produced would be PMPKAK (c) If profits are being maximised, then profits can only be increased by using a different combination of inputs (d) If an extra unit of capital is used, the cost of producing the extra output produced will be rAKMPK (e) Profit maximisation will occur where the marginal rate of substitution is greater than the ratio of prices.