What is the elasticity of substitution for the production function f(K, L) = K2 + L2? O b. o = %3D O c. o = 1 O d. o = 2 O e. o = 4 Clear my choice A firm's cost function is C(q) = 2000 + 10g + 5q². If the firm is a price-taker in a market that is in long-run equilibrium, what quantity does the firm sell? %3D O a. q = 5 O b. q = 10 O c. q = 20 1/14
What is the elasticity of substitution for the production function f(K, L) = K2 + L2? O b. o = %3D O c. o = 1 O d. o = 2 O e. o = 4 Clear my choice A firm's cost function is C(q) = 2000 + 10g + 5q². If the firm is a price-taker in a market that is in long-run equilibrium, what quantity does the firm sell? %3D O a. q = 5 O b. q = 10 O c. q = 20 1/14
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Economics Practice Questions
#### Question 1
**What is the elasticity of substitution for the production function \( f(K, L) = K^{1/2} + L^{1/2} \)?**
- a. \( \sigma = \frac{1}{4} \)
- b. \( \sigma = \frac{1}{2} \)
- c. \( \sigma = 1 \)
- d. \( \sigma = 2 \)
- e. \( \sigma = 4 \)
*Selected Choice: c. \( \sigma = 1 \)*
#### Question 2
**A firm's cost function is \( C(q) = 2000 + 10q + 5q^2 \). If the firm is a price-taker in a market that is in long-run equilibrium, what quantity does the firm sell?**
- a. \( q = 5 \)
- b. \( q = 10 \)
- c. \( q = 20 \)
- d. \( q = 50 \)
*Selected Choice: c. \( q = 20 \)*
### Explanation
For Question 1, we are asked to determine the elasticity of substitution for the given production function \( f(K, L) = K^{1/2} + L^{1/2} \).
- Elasticity of substitution is a measure of the ease with which one factor can be substituted for another in the production process.
- For the Cobb-Douglas production function of the form \( K^aL^b \), the elasticity of substitution \( \sigma \) is typically equal to 1.
- The correct choice is thus c. \( \sigma = 1 \).
For Question 2, the firm's cost function \( C(q) = 2000 + 10q + 5q^2 \) is provided. To find the quantity \( q \) that the firm sells in long-run equilibrium:
- The firm will produce where marginal cost (MC) equals the market price (P). The marginal cost is derived from the cost function.
- In a perfectly competitive market in long-run equilibrium, firms produce where price (P) equals both marginal cost (MC) and average cost (AC), ensuring no economic profit.
-The correct choice here is c. \( q = 20 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ec70b84-8e2a-4846-85d9-f50115a864e8%2F6a8fb8a8-a1e2-4b21-afdb-9660c7666f02%2Flbq1bos_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Economics Practice Questions
#### Question 1
**What is the elasticity of substitution for the production function \( f(K, L) = K^{1/2} + L^{1/2} \)?**
- a. \( \sigma = \frac{1}{4} \)
- b. \( \sigma = \frac{1}{2} \)
- c. \( \sigma = 1 \)
- d. \( \sigma = 2 \)
- e. \( \sigma = 4 \)
*Selected Choice: c. \( \sigma = 1 \)*
#### Question 2
**A firm's cost function is \( C(q) = 2000 + 10q + 5q^2 \). If the firm is a price-taker in a market that is in long-run equilibrium, what quantity does the firm sell?**
- a. \( q = 5 \)
- b. \( q = 10 \)
- c. \( q = 20 \)
- d. \( q = 50 \)
*Selected Choice: c. \( q = 20 \)*
### Explanation
For Question 1, we are asked to determine the elasticity of substitution for the given production function \( f(K, L) = K^{1/2} + L^{1/2} \).
- Elasticity of substitution is a measure of the ease with which one factor can be substituted for another in the production process.
- For the Cobb-Douglas production function of the form \( K^aL^b \), the elasticity of substitution \( \sigma \) is typically equal to 1.
- The correct choice is thus c. \( \sigma = 1 \).
For Question 2, the firm's cost function \( C(q) = 2000 + 10q + 5q^2 \) is provided. To find the quantity \( q \) that the firm sells in long-run equilibrium:
- The firm will produce where marginal cost (MC) equals the market price (P). The marginal cost is derived from the cost function.
- In a perfectly competitive market in long-run equilibrium, firms produce where price (P) equals both marginal cost (MC) and average cost (AC), ensuring no economic profit.
-The correct choice here is c. \( q = 20 \).
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