Q1
Subject:EconomicsPrice: Bought3
Q1. Woozles can be manufactured in either of two types of factory with the following cost functions. A perfectly competitive manufacturer of woozles currently has two factories, one of each type:
C1 = 0.2q12 + 5.2q1 + 25
C2 = q22 + q2 + 9.8
where Ci = total cost function for type i factory, i = 1, 2.
qi = production of type i factory, i = 1, 2.
(a) Market price for woozles is currently 4. What is the profit-maximizing (loss-minimizing) production from each factory?
(b) The manufacturer wants to produce 16.5 woozles. What is the cost-minimizing allocation of this production between the two factories?
Q2. Currently 10 identical bakeries are producing bread in a competitive market. The cost function for a typical bakery is:
Ci = 6qi + 0.01qi2 + 100.
The demand for bread is:
q = 1800 - 100p
(a) What is the short run market supply curve?
(b) What will be the equilibrium price and volume of bread sales in the market?
(c) At the equilibrium of (b) what is the output per bakery? Are bakeries incurring losses, making profits, or breaking even?
(d) The government imposes a $1 per loaf tax on bread (let them eat cake!). In the short
run what will be market volume and price, and output per bakery? Will individual
bakeries suffer a short-run loss, and if so, how much?
(e) What will be the long run response of market price and volume to imposition of the $1 per loaf tax? How many bakeries will remain, and what will be output per bakery?
Q3. Ten competitive sawmills currently supply lumber to a market whose demand q,
depends on lumber price, p, as follows:
q = 3550 - 350p.
The cost function of each mill is identical:
Ci = 5qi + 0.05qi2 + 80 i = 1........10
(a) Determine the market supply curve.
(b) Determine the short run equilibrium market price and output.
(c) Is the equilibrium in (b) also a long run equilibrium? Why or why not?
(d) Technical development changes the cost function of new mills to:
Cj = 5qj + 0.1qj2 + 22.5
Ninety new competitive mills enter the market. What becomes the new short-run equilibrium market price and output? Assume the old mills still operate and that the entry and exit of mills do not affect individual mill cost functions.
(e) What will be the long run market equilibrium price and output? How many mills of what type - new or old - will survive?
Q4. A perfectly competitive constant cost industry contains a number of firms, each of which has the following long-run total cost function, where q is annual output:
TC = 0.01q3 - 1.2q2 + 101q
The market demand curve for the product is:
Q = 7,000 - 20p
where Q is annual industry sales.
(a) Calculate the long-run equilibrium output of the industry.
(b) How many firms are there in the industry in long run?
2.1 A firm claims on its website that it has been in the same location for over 50 years and has lower overhead than other firms because it bought the land 50 years ago when it was inexpensive. It also claims that it charges lower prices than competitors because of its lower overhead. Discuss the logic of these claims.
2.3 Initially, the market price was p = $50, and the competitive firm's minimum average variable cost was $42 while is minimum average cost was $54. Should it shut down? Why or why not? Now suppose the firm's average variable cost increases by $9 at every quantity, while other firms in the market are unaffected.
What happens to its average cost? Should the firm shut down now? Why or why not?
2.4 Should a firm shut down if its revenue is R = $1,500 per week and:
a. its variable cost is VC = $1,100 and its sunk fixed cost is F = $800?
b. its variable cost is VC = $1,600 and its sunk fixed cost is F = $600?
c. its variable cost is VC = $1,100 and its fixed cost is F = $1000 ($800 of which is avoidable
if it shuts down?
2.6 Beta Laundry's cost function is C(q) = 50 + 10q + 2q2.
a. What quantity maximizes Beta's profit if the market price is p? How much does it produce
if p = $70?
b. If the government imposes a specific tax of t = $4, what quantity maximizes Beta's aftertax
profit? Does it operate or shut down?
3.6 In late 2004 and early 2005, the price of raw coffee beans jumped as much as 50% from the previous year. In response, the price of roasted coffee rose about 14%. Similarly, in late 2014 and early 2015, the price of raw beans fell by about 25%, yet the price of roasted coffee fell by only a few percentage points. Why did the roasted coffee price change less than in proportion to the rise in the cost of raw beans?
