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d) Solve numerically for quantity produced and labor and capital demanded when v = 1, w = 1. e) What happens to quantity produced and labor and capital demanded when v increases to 4?

d) Solve numerically for quantity produced and labor and capital demanded when v = 1, w = 1. e) What happens to quantity produced and labor and capital demanded when v increases to 4?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Just part (d) and (e)

### Exercise 3 Suppose that a firm has a cost function given by \( C(q, v, w) = v^{1/2} w^{1/2} q^2 \). **a)** Suppose the firm sells their good in a competitive market, where the price of their good is $10. How much do they produce? **Note**: The answer will be a function of \( v \) and \( w \). **b)** Solve for the firm's contingent demand functions for labor and capital. **c)** Solve for the firm's unconditional demand functions for labor and capital, using the fact that \( l(p, v, w) = l^c(p, v, w) \) and \( k(p, v, w) = k^c(p, v, w) \). **d)** Solve numerically for the quantity produced and labor and capital demanded when \( v = 1 \), \( w = 1 \). **e)** What happens to the quantity produced and labor and capital demanded when \( v \) increases to 4? This problem set involves understanding and utilizing the cost function \( C(q, v, w) = v^{1/2} w^{1/2} q^2 \) to derive various production and demand scenarios for a firm in a competitive market. It requires comprehension of cost functions, contingent demand, and unconditional demand functions in economic models. The exercises test the ability to derive these functions and interpret them numerically under given conditions.
Transcribed Image Text:### Exercise 3 Suppose that a firm has a cost function given by \( C(q, v, w) = v^{1/2} w^{1/2} q^2 \). **a)** Suppose the firm sells their good in a competitive market, where the price of their good is $10. How much do they produce? **Note**: The answer will be a function of \( v \) and \( w \). **b)** Solve for the firm's contingent demand functions for labor and capital. **c)** Solve for the firm's unconditional demand functions for labor and capital, using the fact that \( l(p, v, w) = l^c(p, v, w) \) and \( k(p, v, w) = k^c(p, v, w) \). **d)** Solve numerically for the quantity produced and labor and capital demanded when \( v = 1 \), \( w = 1 \). **e)** What happens to the quantity produced and labor and capital demanded when \( v \) increases to 4? This problem set involves understanding and utilizing the cost function \( C(q, v, w) = v^{1/2} w^{1/2} q^2 \) to derive various production and demand scenarios for a firm in a competitive market. It requires comprehension of cost functions, contingent demand, and unconditional demand functions in economic models. The exercises test the ability to derive these functions and interpret them numerically under given conditions.
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