Consider a Production Function given by the form z=F(K,L)=(K^(0.3) + L^(0.7) )^2 where K is the amount of capital and L is the amount of labor. Further, we assume that K>0 and L>0. Take the first order partial derivative of the production function with respect to capital and labor. What does the first order partial derivative imply? (Hint: Remember the definitions of the variables)

Consider a Production Function given by the form z=F(K,L)=(K^(0.3) + L^(0.7) )^2 where K is the amount of capital and L is the amount of labor. Further, we assume that K>0 and L>0. Take the first order partial derivative of the production function with respect to capital and labor. What does the first order partial derivative imply? (Hint: Remember the definitions of the variables)

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter17: Economic Growth: Resources, Technology, Ideas And Institutions

Section17.2: A Production Function And Economic Growth

Problem 4ST

See similar textbooks

Similar questions

Consider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure meals; the graph of the production function is a line that intersects the vertical axis at a positive amount; this graph is a line with positive slope and passes through the point (4,300)). Can we say that the production function satisfies the law of decreasing marginal returns of labor?True False
Assuming a Cobb-Douglas production function with constant returns to scale, then, as L rises with K and A constant, it will be the case that: a. Both the marginal product of labour and the marginal product of capital will fall b. The marginal product of labour will fall and the marginal product of capital will rise c. Both the marginal product of labour and the marginal product of capital will rise d. The marginal product of labour will rise and the marginal product of capital will fall
The equation below is a production function, Q = (200)L + (100)K – (0.2)L2 – (0.1)K2 , where Q is output, L is labor and K is capital. What is the Marginal Product of Labor of this function?
Suppose that a firm's production function is given by Q = KL(MPK= L and MPL= K), where Q is the quantity of output, K is units of capital, and L is units of labor. The price per unit of labor and capital are $30 and $20, respectively. a. How many units of labor and capital should the firm use if it wants to minimize the cost of producing 600 units of output?
Show using math and logic that for constant returns to scale production functions, MRTS between labor and capital depends only on the K/L ratio, and not the scale of production.