which of the following statements is true?   1. if the marginal product of labour is higher than the marginal product of capital, then the firm uses more labour than capital in the short run.   2.if the wage rate for labour is lower than the cost of capital, then the firm uses more labour than capital in the short run.   3. if for a given amount of initial capital, the production functions means more labour is needed than capital, then the firm uses more labour than capital in the short run.   4. if for a given amount of initial labour, the production function means that more labour is needed than capital, then the firm uses more labour than capital in the short run.

Consider the production function Y=K1/2 N1/2 a. Compute output when K=37 and N=80 b. If both capital and labour double, what happens to output? c. Is this production function characterized by constant returns to scale? Explain. d. Are there decreasing returns to capital? Explain. e. Are there decreasing returns to labour? Explain. f. Write this production function as a relationship between output per worker and capital per worker. Show all your work. g. Let capital per worker be 6. What is output per worker? Now, double capital per worker to 12. Does output per worker more or less than double? h. Does the relation between output per worker and capital per worker exhibit constant returns to scale? Explain/show your work

A firm has two opportunities for a new plant location, one is in China and the other is inMexico. The firm's production function is given by q = L 0.5 K 0.5 , In China, the cost of laboris w=$15 and the cost of capital is r=$5. In Mexico, w=$10 and r=$10. The firm wants toproduce 100 units of output. Which location should the firm choose for their new plant?Explain why.Note: Please round the optimal amounts of capital and labor at each location to the nearest whole number when making your calculations.Hint: cost-minimization rule.

Solve the attahment.

Consider the production function: Y = z.f(K,N,L) where Y is output, z is a parameter capturing technology, K is capital, N is labour and L is the area of land.

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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).

Suppose a firm’s production function is ? = ?2?. a) Determine the labor and capital demand functions. b) Are capital and labor normal or inferior inputs in this production process?

The law of diminishing marginal returns states: Select one: a. As a firm uses more of a variable factor of production, total product (TP) eventually decreases. b. As the size of a plant increases, marginal product (MP) eventually decreases. c. As a firm uses more of a variable factor of production, its average cost (AC) eventually decreases. d. As a firm uses more of a variable factor of production, with a given quantity of the fixed factor of production, the MP of the variable factor eventually decreases.

Output is produced according to Q = 4LK, where Lis the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5, then the cost-minimizing combination of K and L capable of producing 32 units of output is: L = 2 and K = 4. L = 4 and K = 2. L = 1 and K = 8. L = 8 and K = 1. L = 2 and K = 2.