Download Q1 (25 points) You are the production manager of a plant that

ECON 303
Fall 2003
Midterm 3
Dr. Cary Deck
This exam consists of 4 written problems worth 25 points each. Your exam should
contain 5 pages. Please write your name on the top of each page. Answer each question
as best you can. Where appropriate you must show work in order to receive full credit.
The exam is closed book. If you have any questions please raise your hand and someone
will come to you. There is no talking allowed during the exam. The use of electronic
devices other than approved calculators is prohibited. You have one hour and twenty
minutes to complete this exam. Exams will not be accepted after the end of the exam has
been announced.
Name:___________
Score:____________
Q1 (25 points) You are the production manager of a plant that produces roads. A ton of
road can be produced using labor and capital according to the production function
f(L,K)=L1/3K1/2. You are under contract to hire 27 workers each being paid $5. The
capital input costs only v=$1 per unit.
There is a potential customer who is looking for someone to lay 30 tons of road. How
much capital would you have to buy to complete this project? (3 points)
Q=30 and L=27 so 30=3k1/2 or 10=k1/2 or k=100
What would your cost be to lay 30 tons of road? (3 points)
Cost =wL+vK=27*5+1*100=235
Another potential customer wants to lay 15 tons of road. If you do not get the first
contract, what would be your cost for this project? (4 points)
Q=15 so 15=3k1/2 or 5=k1/2 or k=25.
Cost =wL+vK=27*5+1*25=160
If you got both contracts what would be your cost? (4 points)
Q=45 so 45=3k1/2 or 15=k1/2 or k=225.
Cost =wL+vK=27*5+1*225=360
The first customer is willing to pay $450 while the second one is willing to pay $150.
Which contracts should you accept and why? (4 points)
Profit from 1 only = 450-235=215
Profit from 2 only = 150-160= -10
Profit from 1 and 2 =450+150-360=240.
The biggest profit is to accept both contracts.
What is the equation for your marginal cost of a unit of road? (4 points)
q=3k1/2 or k=q2/9. Hence TC=wL+vK=135+ q2/9. Thus MC=2q/9.
Explain why marginal cost is increasing in output. (3 points)
Since L is fixed, MPk is falling as more capital is used. Therefore, to make extra units of
output a larger and larger amount of capital is required.
Q2. (25 points) You own a company that produces hog shoes, which are hog shaped
slippers that squeal when the wearer walks. Your total cost for hog shoes is
TC=2q2+q+30. Realizing the potential for such sounds to help out Coach Heath and the
Razorbacks, demand for this product is given by P=481-2Q.
Your company is a monopolist. List some potential barriers to entry that your company
or other monopolists in other industries might have. (3 points)
Barriers include sole ownership of a resource, large set up or fixed cost (natural
monopoly), patents and copyrights, and social concerns.
How many hog shoes should you produce and what price should you charge? (3 points
each) What is your maximum profit? (4 points)
Firm wants to produce where MR=MC. MR=481-4Q and MC=4q+1. Thus we have
481-4Q=4Q+1 or Q=60. From Demand we know that the price for 60 units will be
P=481-2(60)=361. The firms profits are TR-TC =361*60-2(60)2-60-30=14370.
Students protest that the monopoly is reducing social welfare. How much higher are your
prices than they would if your firm was competitive? How many fewer hog shoes are
you producing than if your firm was competitive? (2 points each)
The efficient spot is where P=MC or 481-2Q=4Q+1 or Q=80. The price would be 4812(80)=321. So the monopolist is reducing the quantity by 20 and increasing the price by
40.
What is the dead weight loss associated with your firm being a monopolist? (3 points)
The MC of q=60 is 241. Thus DWL=.5*(80-60)*(361-241)=$1,200.
If you could practice perfect price discrimination, how many units would you produce
and what would be the deadweight loss to society? (3 points) What would be the
consumer surplus? (2 points)
A perfect price discriminating monopolist charges each buyer the most that buyer is
willing to pay. Hence DWL=0 and CS=0.
Q3. (25 points) There are 6 competitive firms in an industry, each with TC= q2+2q+100.
What are the shut down price and the break even price for a firm in this industry? (3
points each) Explain how a firm could want to operate even if it would lose money by
doing so. (4 points)
Breakeven price is where ATC and MC intersect. ATC=q+2+100/q and MC=2q+2.
Thus the breakeven quantity is where q+2+100/q = 2q+2 or 100/q=q or q=10. ATC for
10 units is 10+2+100/10=22. the breakeven price is 22.
The shutdown price is where AVC=MC. AVC=q+2. Thus the shutdown quantity is
where q+2 = 2q+2 or q=0. MC for 0 units is 2. The shutdown price is 2.
A firm would choose to operate even if it was loosing money if it is covering its variable
costs. If the firm shuts down it will still have to pay its fixed costs so as long as it covers
its variable costs the firm is doing better than shutting down.
What is the equation for the market supply curve? (3 points)
MC=2q+2. For a competitive firm MR=P and the Firm sets MR=MC so we have
P=2q+2 or q=(P-2)/2. With 6 firms the market quantity is 6*(P-2)/2 or Q=3P-6.
If demand is given by P=34-Q, what will be the market price in the short run? (2 points)
The price is where Supply and Demand cross. That is where 34-Q=(Q+6)/3. This gives
Q=24 and thus P=10.
Assume that the fixed cost is due to a government bribe that must be paid so that it cannot
be avoided even in the long run. Also, assume that entry or exit in this market will not
impact input prices. What will be the market quantity in the long run? (2 points) Will
this market be served by more or fewer firms than the original 6? (1 point) What will be
the profits of the firms in this industry? (2 points)
The free entry and exit assumption assures that long run profits are zero. In the long run
P=22, so from demand we know that 22=34-Q or Q=12. The starting price was 10,
which is below the breakeven price so there will be exit, pushing supply back and pushing
price up to 22.
If government corruption were cleaned up, meaning that bribes no longer had to be paid,
what would happen to short run supply? (1 points) What would happen to long run
profits? (1 point) Why? (3 points)
The bribe was a fixed cost so it would have no impact on short run supply. However, this
would increase profits causing other firms to enter pushing out the supply curve until
profits returned to zero.
Q4. (25 points) You run a consulting group and you need two types of labor, skilled (s)
and unskilled (u). Skilled labor costs 16 while unskilled labor costs only 2. Output is
given by f(s,u)=s2/3u2/3. What type of returns to scale does this production function
exhibit? Verify your answer. (2 points).
f(1,1)=1 and f(8,8)=16. Since increasing the inputs by 8 lead to a more than 8 fold
increase in output, the production function exhibits increasing returns to scale.
If you want to produce 64 units of output how much of each labor type should you use?
(4 points) Is this a long term or a short term problem? (1 point) Why? (2 points)
This is a long run problem as the firm is free to choose both labor and capital. The firm
wants to set the RTS=price ratio which in this problem means u/s=16/2 or u=8s. So 64=
s2/3(8s)2/3 or 16=s4/3 or s = 8 and hence u = 64.
Congress has decided that $2 is just too low of a wage and is considering increasing the
minimum wage. As a result, the unskilled workers would receive 4 per hour. To produce
64 units, how many unskilled workers would you hire if the minimum wage was raised?
(4 points)
Now setting RTS=price ratio would give u=4s. So we would have 64 = s2/3(4s)2/3
Or s=211/4 and u=219/4.
Your rival uses a different production function. Specifically, they always put workers in
teams so output is f(s,u)=min(4s,2u). How many of each type of worker would they
employ to make 64 units of output if the minimum wage is not raised? (4 points) How
would their choice change if the minimum wage is raised? (2 points)
Given their production function they will use 4s=64 and 2u=64 or u=32 and s= 16.
Notice this did not depend on the wage rates so your rival would not change their hiring
choices if the minimum wage increased.
A university approaches you about sending your skilled workers to their executive MBA
program. For an additional $16 per worker, each skilled worker can attend the program.
With this additional human capital your production function is f(s,u)=s1u1. If you send
your skilled workers to the program, what happens to the marginal product of your
unskilled workers? (2 points) Why might this be the case? (1 point)
Your original MPu=2/3s2/3u-1/3. Your new MPu=s. For any non-negative amount of
skilled and unskilled labor you hire the marginal product of unskilled workers will
increase as 2/3s2/3u-1/3 < s. Perhaps the training makes the skilled workers better able to
manage their workers or allows them to organize tasks more efficiently.
If you want to produce 64 units should you send your workers to the executive MBA
program? (3 points) Assume that the minimum wage increase did not pass Congress.
Without the executive MBA you cost to produce 64 units would be 16*8+64*2=256. If
you send the workers to the program you would only need s=2 and u=32 which would
costs 32*2+2*32=128. So yes you should send your skilled workers to the program
because it will lower your costs. To see that you would only need s=2 and u=32 you
have to solve the cost minimization problem. Setting RTS=price ratio gives u/s=32/2.
Notice the cost of a skilled worker is now 16 wage +16 training cost. To make 64 units
would require u*s=54 or 16s2=64 or s=2