The paradise Shoes Company has estimated 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 = 400-25P. The company is currently producing 1000 pairs of shoes weekly and is considering expanding its output to 1200 pairs of shoes weekly. To do this, it will have to lease another shoe-making machine ($2000 per week fixed payment until the lease period ends).
Show all of your calculations and processes. Describe your answer for each item below in complete sentences, whenever it is necessary.
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 1000 pairs to 1200 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 1200 pairs per week. State all assumptions and qualifications that underlie your recommendation.