Trotter Inc is a polling company. Trotter uses both labor, L, (measured in hours worked) and capital, K, (measured in phone lines) to conduct surveys. The production function of Trotter’s is given by Q=10L^0.25 K^0.25 where Q is measured in surveys completed per hour. The price of a unit of L is $16 per hour and the price of a unit of K is $1 per hour. Trotter’s has additional fixed costs of $227 per hour. For parts (a) – (b) below assume that the number of phone lines is fixed in the short run. In particular, Trotter's has 16 phone lines (so K = 16). This results in additional fixed costs in the short run of $16 (ie in addition to the 227). a) In the short run what is Trotter’s (compensated) demand curve for labor? What is the variable cost curve? What is the total cost curve? b) In the short run, what is the marginal cost curve of Trotter’s? What is the average cost curve? What is the optimal size of the firm? Illustrate the short run marginal and average cost curves. For parts (c)- (d) assume that Trotter’s number of phone lines is variable in the long run. c) In the long run what is Trotter’s (compensated) demand curve for labor? What is the (compensated) demand for capital? What is the variable cost curve? What is the total cost curve? d) In the long run what is Trotter’s marginal cost curve? What is the average cost curve? d) What is the (approximate) optimal scale in the long run? Let’s compare the average cost curves in the short and long runs. You may assume that at every quantity the long run average cost is less than or equal to the short run average cost.
Trotter Inc is a polling company. Trotter uses both labor, L, (measured in hours worked) and capital, K, (measured in phone lines) to conduct surveys. The production function of Trotter’s is given by Q=10L^0.25 K^0.25 where Q is measured in surveys completed per hour. The price of a unit of L is $16 per hour and the price of a unit of K is $1 per hour. Trotter’s has additional fixed costs of $227 per hour.
For parts (a) – (b) below assume that the number of phone lines is fixed in the short run. In particular, Trotter's has 16 phone lines (so K = 16). This results in additional fixed costs in the short run of $16 (ie in addition to the 227).
a) In the short run what is Trotter’s (compensated)
b) In the short run, what is the marginal cost curve of Trotter’s? What is the average cost curve? What is the optimal size of the firm? Illustrate the short run marginal and average cost curves.
For parts (c)- (d) assume that Trotter’s number of phone lines is variable in the long run.
c) In the long run what is Trotter’s (compensated) demand curve for labor? What is the (compensated) demand for capital? What is the variable cost curve? What is the total cost curve?
d) In the long run what is Trotter’s marginal cost curve? What is the average cost curve? d) What is the (approximate) optimal scale in the long run? Let’s compare the average cost curves in the short and long runs. You may assume that at every quantity the long run average cost is less than or equal to the short run average cost.
Step by step
Solved in 5 steps with 28 images
