Transcript Homework 6 Answer Key

Homework 6 Answers
Question 1: Which is not a characteristic of a perfectly competitive industry? _B__
a. Marginal revenue is equal to the market price
b. Products from different firms in the industry are complements
c. Firms can easily enter and/or exit the industry (in the long run)
d. Firms and consumers have perfect information
Question 2: If average variable cost exceeds the market price, a firm should: __C_
a. Increase production
b. Decrease production but keep producing at positive levels
c. Shut down
d. Continue producing at current level
Question 3: In the long run, economic profits in a competitive industry are equal
to: _C_
a. Accounting profits
b. Total revenue
c. Zero
d. The absolute value of fixed costs
Question 4: Efficiency of competitive equilibrium
a. Why is a competitive equilibrium efficient in the short run?
MR=MC. Cost of last unit produced is exactly equal to what buyers
are willing to pay for it
b. What are the benefits to society as a whole of competitive
equilibrium in the long run?
Output is produced in the least cost way (P=min LAC). Producers earn
only normal profit so that all benefits are captured by consumers
Question 5. On the following graph of a firm’s costs in the short run,
label the curves and indicate the supply function using a heavier line or
different color ink
Question 7 Suppose that bicycles are produced by a perfectly competitive, constant
cost industry. Which of the following will have a larger effect on the long-run price of
bicycles: 1) a government program to advertise the health benefits of bicycling or 2) a
government program that increases the demand for steel, an input into the manufacture
of bicycles that is produced in an increasing cost industry? Briefly explain why.
Advertisement about health benefits: Since the supply curve faced by the individual
firm is elastic, the advertisement (which shifts the demand curve out) will increase
quantity but leave price unchanged.
Program that raises price of steel: The result will be a shift in the long-run
supply curve. Price of bicycles will increase and quantity will decrease.
Question 8 You are the owner/manager of a small competitive firm that manufactures house paints.
You and all your 1000 competitors have a total cost curve given by TC=8+2Q+2Q2 and the industry is in
long run equilibrium. Now you are approached by an inventor who holds a patent on a process that will
reduce your costs by half at each level of output.
a) What is the most you would be willing to pay for the exclusive right to use this invention?
The most you would be willing to pay would be the difference between your profit with the
technology and your profit without the technology. Since profit without the technology is zero
(market is in long run equilibrium), you would be willing to pay up to the total value of your profit
with the technology. To find profit, you need to find the profit maximizing level of Q under the new
technology and equilibrium market price, and then use that to calculate total revenue (at equilibrium
market price) and total cost (with new cost curve).
Step 1. Find the equilibrium market price. You are not given P, but you are told that the market is in
long run equilibrium which means that P=minimum long run average cost (min LAC). Therefore, you
can find the Q that minimizes LAC by setting ∂LAC/∂Q=0 and plugging that Q into the LAC function to
get P. Remember that you want to find the equilibrium price in the market without the new
technology, so you use the original cost function. LAC=TC/Q = (8+2Q+2Q2 )/Q = 8/Q+2+2Q. ∂LAC/∂Q
= -8/Q2 + 2. Set equal to 0 => 2 = 8/Q2=>2Q2=8 =>Q2=4=>Q =2. Plug 2 into the LAC function (8/Q+2+2Q)
to get P=> 4+2+4=10.
Question 9 The government of Philadelphia is currently debating whether
they should implement a tax on soda. The hourly supply function for soda is
P = 1+ .5QS and the hourly demand function is P = 20-1.5QD. Suppose the
government is considering a tax of $4 on each unit that the supplier sells.
Graph the supply and demand functions for soda in the space below (on
the same graph
P
Stax = 5+.5Q
S=1+.5Q
Pc =8.75
P*=5.75
Tax born by
consumers
Tax born by producers
Ps = 4.75
5
Qt =7.5 Q*=9.5
15
Q
Calculate and label on the graph:
No-tax equilibrium price and quantity of soda (P*, Q*)
Supply = demand => 1+.5Q=20-1.5Q =>Q*=9.5 and P*=5.75
Price consumers pay with the tax (Pc)
At Qtax=7.5, Pc = 20-1.5(7.5) = 8.75
Price sellers receive with the tax (Ps)
Qtax=7.5, Ps=1+.5(7.5) = 4.75
Quantity sold with the tax (Qt)
With the tax on supply, the new supply curve will be P=5+.5Q. New equilibrium will be
5+.5Q =20-1.5Q => Qtax=7.5
Indicate the size of the tax and the tax burden born by producers and consumers on the
graph
Tax = 7.5*4= 30. Consumers pay 7.5*3 = 22.5 and producers pay 7.5*1 = 7.5