Labor Economics
7th Edition
ISBN: 9780078021886
Author: George J Borjas
Publisher: McGraw-Hill Education
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Question
Chapter 3, Problem 4P
(a)
To determine
Explain the effect of substitution effect in firm’s employment and capital change.
(b)
To determine
Explain the direction in which the scale effect changes the firm’s employment and capital stock.
(c)
To determine
Explain that preference of firm in the selection of labor and capital.
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Juan Valdez owns a coffee farm in Colombia. His production function is:
f(x1,x2)=(x1−1)^0.25 x2^0.5
Assume the price of input 1 is r and the price of input 2 is w.
(a) Write down an expression for the technical rate of substitution.
(b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce.
(c) Find Juan's cost function.
(d) What is the supply function of Juan's firm?
Input either "increase" or "decrease" where relevant:
An increase in the prices of inputs will cause the equilibrium price to ....... and the equilibrium quantity to .....
1. Juan Valdez owns a coffee farm in Colombia. His production function is:
f (x1, x2) = (x1 – 1)0.25 x9-5.
Assume the price of input 1 is r and the price of input 2 is w..
(a) Write down an expression for the technical rate of substitution.
(b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan
wants to produce.
(c) Find Juan's cost function.
(d) What is the supply function of Juan's firm?
2. Show that the profit function is convex in (p, w).
3. Find the profit function for the Cobb-Douglas production function f(¤1, 12) = Ax†' x"
with A > 0, a1, ¤2 > 0 and a1 + a2 0, B > 0, 0 < a < 1, and 0 + p< 1.
6. Find the profit function for the CES production function.
7. Verify Hotelling's Lemma for the CES production function with B < 1.
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