mework%202.pdf 1 / 2 100% 1. Suppose the production function is Cobb-Douglas, Q-L1/2K3/2. Marginal products are MPL-0.5L-1/2K3/2 and MPK=1.5L1/2K1/2. Answer: (a) Holding capital constant, is marginal product of labor increasing, decreasing or constant? Explain. (b) Holding labor constant, is marginal product of capital increasing, decreasing or constant? Explain. (c) What is the expression for the marginal rate of technical substitution of labor for capital? (d) Is the MRTSL.K increasing, deacreasing, or constant as more labor is used? Explain. (e) Does this technology exhibit increasing, constant, or decreasing returns to scale? Explain.way to produce @ units of output. 4. Suppose the production function is Q-0.1K/213/4. Marginal products are MPL- 0.075K ?L-1/4. and MPk-0.05K-/2L3/4. Rental rate of capital is $1, wage is $2. (a) In the short run capital is fixed at K=100. How much labor is needed to produce Q units of output? (b) Write down the short run total cost and average cost functions, (c) In the long run all inputs are variable. What is the cheapest way to produce ] unit of output? (d) How much does it cost to produce 1 unit of output in the long run?Zoom X G manchester metropol Meet - vink-exws-xih e ECON 281 (LEC A01 F X Homework 2.p loads/Homework%202.pdf 2 / 2 100% This problem set is not for sharing outside of class 2. A firm has two plants where it can make its output: one in Edmonton and one in Calgary. Edmonton plant's technology can be described as QE-min (L, 2K) and Calgary plant's technology is Qc-min (2L, K) . (a) On one graph draw two isoquants: one for producing 40 units of output in Edmonton (label it QE-40), and another one for producing 40 units of output in Calgary (label it Qc-40). (b) On the same graph draw a third isoquant representing the whole firm's technological capabilities for producing 40 units of output, if that output can be split between the two plants in any manner. That is, the 40 units can be produced all in Calgary, or all in Edmonton, or half-half, or 10-30, or any other way. Label this isoquant Q-40. (c) Is this firm's technology convex? Explain.X (G) manchester metropol x Meet - vik-exws-xih x @ ECON 281 (LEC A01 F. X 5 Home /Homework%202.pdf 2 / 2 100% 3. The production function is given by Q-min ( L, 2K) . (a) Does this production function exhibit increasing, decreasing, or constant returns to scale? (b) Suppose price of labor is I and price of capital is 1. What is the cheapest way to produce 10 units of output? Illustrate with a graph. (c) If input prices are w and / respectively, derive an expression for the cheapest way to produce 10 units of output. (d) If input prices are w and r respectively, derive a more general expression for the cheapest way to produce O units of output