Consider a Cobb-Douglas production function with three inputs. K is capital (the numbe achines), L is labor (the number of workers), and H is human capital (the number of coll =grees among the workers). The production function is Y=K2/6 L3/6 H1/6 Derive an expression for the marginal product of labor. How does an increase in the amoun man capital affect the marginal product of labor? (Hint: The marginal product of labor MP und by differentiating the production function (Y) with respect to labor (L)) Derive an expression for the marginal product of capital. How does an increase in the amo human capital affect the marginal product of capital? (Hint: The marginal product of capita
Consider a Cobb-Douglas production function with three inputs. K is capital (the numbe achines), L is labor (the number of workers), and H is human capital (the number of coll =grees among the workers). The production function is Y=K2/6 L3/6 H1/6 Derive an expression for the marginal product of labor. How does an increase in the amoun man capital affect the marginal product of labor? (Hint: The marginal product of labor MP und by differentiating the production function (Y) with respect to labor (L)) Derive an expression for the marginal product of capital. How does an increase in the amo human capital affect the marginal product of capital? (Hint: The marginal product of capita
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.2P
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Transcribed Image Text:2. Consider a Cobb-Douglas production function with three inputs. K is capital (the number of
machines), L is labor (the number of workers), and H is human capital (the number of college
degrees among the workers). The production function
Y = K2/6 L3/6 H1/6
a) Derive an expression for the marginal product of labor. How does an increase in the amount of
human capital affect the marginal product of labor? (Hint: The marginal product of labor MPL is
found by differentiating the production function (Y) with respect to labor (L))
b) Derive an expression for the marginal product of capital. How does an increase in the amount
of human capital affect the marginal product of capital? (Hint: The marginal product of capital
MPK is found by differentiating the production function (Y) with respect to capital (K)).
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