Marginal product and diminishing returns. (13 points) Adapted from GLS Ch6.app P2. A more general...

Question

Marginal product and diminishing returns. (13 points) Adapted from GLS Ch6.app P2. A more general form of the Cobb-Douglas production function is given by Q = AKaL ß where A, a, and ß are positive constants. Expressing the exponents in terms of a and ß allows us to more generally describe what happens for all functions of this form. (a) (3 points) Solve for the marginal products of capital and labor. Remember, you can treat A, a, and ß as numbers. The same rules of derivatives apply (the term gets multiplied by the exponent, and the exponent drops by 1). (b) (3 points) Use calculus to show how the marginal product of labor changes as labor increases by a small amount. Use calculus to show how the marginal product of capital changes as capital increases by a small amount. (c) (4 points) For what values of a and ß will the production function exhibit diminishing marginal returns to capital and labor? (You may assume that the values of capital and labor are positive quantities, a and ß are positive, and A is positive. ) (d) (3 points) Solve for the marginal rate of technical substitution when a = 1 3 , ß = 2 3 and there are 2 units of capital and 5 units of labor.

David · Accepted Answer

Marginal product and diminishing returns. (13 points) Adapted from GLS Ch6.app P2. A more general 
form of the Cobb-Douglas production function is given by Q = AKaL ß where A, a, and ß are positive 
constants. Expressing the exponents in terms of a and ß allows us to more generally describe what 
happens for all functions of this form. 
(a) (3 points) Solve for the marginal products of capital and labor. Remember, you can treat A, a,

Marginal product and diminishing returns. (13 points) Adapted from GLS Ch6.app P2. A more general form of the Cobb-Douglas production function is given by Q = AKaL ß where A, a, and ß are positive...

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment