The total and marginal cost functions for a typical soft coal producer are: TC =
ID: 1181757 • Letter: T
Question
The total and marginal cost functions for a typical soft coal producer are:
TC = 75,000 + 0.1q2 and MC = 0.2q
where q is measured in railroad cars per year. The industry consists of 55 identical producers.
The market demand curve is:
QD = 140,000 - 425P,
where P is the price per carload and QD is total market demand. The market can be regarded as competitive.
a. Calculate the short run equilibrium price and quantity in the market.
b. Calculate the quantity that each firm would produce.
c. Calculate the firm's profit (or loss).
d. Calculate producer surplus, consumer surplus, and total surplus at the equilibrium
(Hint: if you draw a figure of market demand and market supply curves, it will be easier for you to solve for the surplus.)
Question 2 (20 points)
Suppose that the total cost function of a firm is given as
TC = 1,000 + 10Q2
a. Determine the output level that minimizes average total cost (ATC). At this output level, find TC, ATC, MC.
b. Determine the output level that minimizes average variable cost (AVC). At this output level, find TC, ATC, MC.
Question 3 (20 points)
Suppose Race Car Motors (RCM) has two divisions
Explanation / Answer
In this market the firm will maximize profits when P=MC=MR. So the market demand would be
QD=140000 -425(0.2Q), QD=55Q
55Q=140000-85Q
140Q=140000
Q=1,000, P= 0.2 x 1000 = 200.
QD= 55 x 1000 = 55,000, market price= 55000=140000-425P=85000/425=200
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