SECTION1: MICROECONOMICS Q1. Given the following Cobb-Douglas production functio

Question

SECTION1: MICROECONOMICS Q1. Given the following Cobb-Douglas production function,O-AK L (a) Derive the marginal product of capital. (S Points) (b) Suppose -?.5, As 10 units, Ke 100, and L-50 units, derive the marginal product of labor Points) Q2. (a) Suppose the per unit prices of capital and labor are $20 and $10 respectively, derive the isoquant and isocost (2 Points) (b)What will be the optimal combination of labor and capital? (2 Points) (c) Show and explain what will happen if the per unit price of labor goes up to $20 (you must show the changes in the isocost and isoquant, and discuss the substitution effect) (2 Points) (d) What are the average products of labor and capital? (4 points) Q3. Imagine that the inverse demand function of a monopolist is: P-200-50 (a) What is the marginal revenue of the monopolist? (2 Points) Suppose the cost function of the monopolist is specified as follows: (b) What is the marginal cost of the monopolist? (4 Points) (c) What will be the profit-maximizing quantity of the monopolist? (4 Points) Q4. A consumer has $1500 to spend on two goods, widgets and gadgets; derive the budget constraint it the prices of widgets and gadgets are $10 and $15 respectively. (5 Points) (b) Show the substitution effect if the price of widgets increase to $15. (5 Points) Q5. A disgruntled employee has sued your company for wage discrimination. An economist has provided you the following results: Coefficient 1000 389.17 2.125 5.318 -24.132 57.87 98.5 Standard error Observations Constant Hispanics Blacks Others 66.09 1.214 0.962 12.92 R2 Assuming that constant is for whites, how will you interpret the results for the jurors? (10 Poin GO TO THE NEXT PAGE

Explanation / Answer

Questions No .1

Q = AK^aL^1-a

dQ/dK = a.AK^a-1 L^1-a

    MPk = ( AK^aL^1-a) / K

                 = a ( Q/K)

MP L or dQ/dL

           = AK^a (1-a) L^1-a-1

                  =    (1-a) ( AK^a L^1-a / L

       = ( 1-a) Q/L

MPL = ( 1- 0.5) (10* 100^0.5 *50 ^0.5 / L

           = 0.5 ( 100)(7.07) /L

          = 353.5/L

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