Answer to Question #143493 in Macroeconomics for Eric

Question

2. Hale and Heart Limited (HH) is a small distributor of B&Q Foodstores, Inc., in the highly competitive health care product, papaya extract, is $10. HH’s total cost (TC) function is given as Qd=100+2Q+0.01Q2 .
a. What is the firm’s profit-maximizing level of output? What is the firm’s profit at the profit-maximizing output level? Is HH in short-run or long-run competitive equilibrium? Explain.
b. Diagram your answer in above
c. At P=$10, what is HH’s break-even price and output level?
d. What is HH’s long-run break-even price and output level?
e. What is HH’s shutdown price and output level? Does this price-output combination constitute a short –run competitive equilibrium? Explain.

Answer 1

a. The firm’s profit-maximizing level of output is:

P = MC,

MC = TC'(Q) = 2 + 0.02Q,

2 + 0.02Q = 10,

Q = 400 units.

The firm’s profit at the profit-maximizing output level is:

$TP = P×Q - TC = 10×400 - (100 + 2×400 + 0.01×400^2) = 1,500.$

HH is in short-run competitive equilibrium, becaise its profit is positive.

b. The answer above can be depicted as the marginal cost curve intersecting the demand curve above the average total cost curve.

c. At P=$10 the HH’s break-even output level is:

$Q = \frac{100} {10 - (2 + 0.01Q)},$

$8Q - 0.01Q^2 - 100 = 0,$

$Q^2 - 800Q + 10,000 = 0,$

Q1 = (800 + 774.6)/2 = 1174.6 units,

Q2 = (800 - 774.6)/2 = 12.7 units.

d. HH’s long-run break-even price is lower and output level is higher.

e. HH’s shutdown price and output level is at P = AVC or 0.01Q + 2 = 10,

Q = 800 units.

This price-output combination does not constitute a short–run competitive equilibrium.