Joe's coffee house operates under the production function Q (L, K) = L²K², where L is the number of worker hours and K is the number of coffee machine hours. a. What happens to the marginal product of labor as Joe uses more L, holding K constant? Justify using derivative(s). b. What happens to the marginal rate of technical substitution of L for K as Joe moves from left to right along an isoquant? Justify using derivative(s). c. In general, explain the key differences between diminishing marginal product of labor and diminishing marginal rate of technical substitution of labor for capital. In your explanation, consider how MPL and MRTS both essentially measure how much an additional unit of labor is worth to production. Also consider what is held constant and what is changing for each as the firm uses more labor.
Joe's coffee house operates under the production function Q (L, K) = L²K², where L is the number of worker hours and K is the number of coffee machine hours. a. What happens to the marginal product of labor as Joe uses more L, holding K constant? Justify using derivative(s). b. What happens to the marginal rate of technical substitution of L for K as Joe moves from left to right along an isoquant? Justify using derivative(s). c. In general, explain the key differences between diminishing marginal product of labor and diminishing marginal rate of technical substitution of labor for capital. In your explanation, consider how MPL and MRTS both essentially measure how much an additional unit of labor is worth to production. Also consider what is held constant and what is changing for each as the firm uses more labor.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Joe's coffee house operates under the production function Q (L, K) = L²K², where L is the
number of worker hours and K is the number of coffee machine hours.
a. What happens to the marginal product of labor as Joe uses more L, holding K constant?
Justify using derivative(s).
b. What happens to the marginal rate of technical substitution of L for K as Joe moves from left
to right along an isoquant? Justify using derivative(s).
c. In general, explain the key differences between diminishing marginal product of labor and
diminishing marginal rate of technical substitution of labor for capital. In your explanation,
consider how MPL and MRTS both essentially measure how much an additional unit of labor
is worth to production. Also consider what is held constant and what is changing for each as
the firm uses more labor.
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