The Paradise Shoes Company has estimated its weekly TVC function from data collected over the past several months, as TVC = 3450 + 20Q + 0.008Q2 where TVC represents the total variable cost and Q represents pairs of shoes produced per week. And its demand equation is Q = 4100 – 25P. The company is currently producing 1,000 pairs of shoes weekly and is considering expanding its output to 1,200 pairs of shoes weekly. To do this, it will have to lease another shoe-making machine ($2,000 per week fixed payment until the lease period ends).
a. Describe and derive an expression for the marginal cost (MC) curve.
b. Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes).
c. What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output.
d. Discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. State all assumptions and qualifications which underlie your recommendation.
(Please show all your calculations and process. Describe your answer for each question in complete sentences, whenever it is necessary.)