The economy is populated by two firms. One firm produces cars (c), the other produces beans (b). The production function of each firm i = {c,b} is Y; = KL Cars are capital intensive, hence ce > os. The price of cars is pe and the price of beans is p. Firms take all prices as given. The unit cost of labor is w and the unit cost of capital is r. The total amount of labor and capital in the economy are, respectively, L and K. 1. Write down the optimality condition for capital and labor of each firm 2. Derive the capital-to-labor ratio of each firm
The economy is populated by two firms. One firm produces cars (c), the other produces beans (b). The production function of each firm i = {c,b} is Y; = KL Cars are capital intensive, hence ce > os. The price of cars is pe and the price of beans is p. Firms take all prices as given. The unit cost of labor is w and the unit cost of capital is r. The total amount of labor and capital in the economy are, respectively, L and K. 1. Write down the optimality condition for capital and labor of each firm 2. Derive the capital-to-labor ratio of each firm
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.4P
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Plz give answer 1 and 2
![The economy is populated by two firms. One firm produces cars (c), the other
produces beans (b). The production function of each firm i = {c, b} is Y;
K L-4. Cars are capital intensive, hence a > an. The price of cars is pe
and the price of beans is po. Firms take all prices as given. The unit cost of
labor is w and the unit cost of capital is r. The total amount of labor and
capital in the economy are, respectively, L and K.
1. Write down the optimality condition for capital and labor of each firm
2. Derive the capital-to-labor ratio of each firm
3. Define an equilibrium for this economy
4. The quantities used by the firm producing cars as a fraction of the total
quantities in the economy are K. = nKK and Le = n1,L, for some values
0 < nK <1 and 0 < nL < 1. Use the labor and capital market clearing to
find analogous expressions for K, and Lp. How many equilibrium condi-
tions are you left with? What are equilibrium values you are left to solve
for?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50e56197-12bc-4435-9d06-afde5115b3bd%2F803aac54-1114-48b4-93af-b353580e51e4%2F1yodst2_processed.png&w=3840&q=75)
Transcribed Image Text:The economy is populated by two firms. One firm produces cars (c), the other
produces beans (b). The production function of each firm i = {c, b} is Y;
K L-4. Cars are capital intensive, hence a > an. The price of cars is pe
and the price of beans is po. Firms take all prices as given. The unit cost of
labor is w and the unit cost of capital is r. The total amount of labor and
capital in the economy are, respectively, L and K.
1. Write down the optimality condition for capital and labor of each firm
2. Derive the capital-to-labor ratio of each firm
3. Define an equilibrium for this economy
4. The quantities used by the firm producing cars as a fraction of the total
quantities in the economy are K. = nKK and Le = n1,L, for some values
0 < nK <1 and 0 < nL < 1. Use the labor and capital market clearing to
find analogous expressions for K, and Lp. How many equilibrium condi-
tions are you left with? What are equilibrium values you are left to solve
for?
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