Download Exam 3 Fall 2004

ECON 303
Fall 2004
Exam 3
Dr. Cary Deck
This exam consists of 2 written problems worth 30 points each and 1 written problem
worth 40 points. Your exam should contain 4 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. (30 points) You manage a firm that produces Thanksgiving decorations using labor
and capital according to the following production function: f(L,K)=L1/2K2/3.
Demonstrate what kind of returns to scale your production function exhibits. (3 points)
What will be true about the shape of your firm’s average total cost curve?
Explain. (4 points)
f(1,1)=1. f(2,2)= 21/222/3=27/6>2=2*f(1,1) so this has increasing returns to scale. With
increasing returns to scale, doubling inputs will double output while costs will double.
Therefore, the average cost will fall.
Assume that w=12 and v=4. Find the equation for TC. (6 points)
Is this a long run or a short run problem? Explain. (3 points)
Since nothing is fixed this is a long run problem. Setting the RTS=w/v and simplifying we
have K/4=L. So q= L1/2K2/3= (K/4)1/2K2/3=.5*K7/6 or K=(2q)6/7. Therefore
TC=wL+vK=12*K/4+4K=7K=7(2q)6/7.
Assuming that the market for Thanksgiving decorations is competitive, what assumption
ensures that your firm’s profits will be 0 in the long run? Explain. (4 points)
The assumption of free entry and exit forces long run profits to 0 for a competitive firm.
If there is a positive profit, firms will enter the market pushing prices down and profits
down. Similarly if there is a loss firms will leave the market pushing prices and profits
up.
A new proprietary technology is available for producing Thanksgiving decorations. If
your firm adopts the technology then your production function would be f(L,K) =
min(2L,8K). If you need to produce 128 units, how much would you be willing to pay to
lease this new technology? (5 points)
To make 128 units with this new technology, you would need 2L=128 and 8K=128 or
L=64 and K=16. This would cost 12*64+4*16=$832. With the old technology the cost
would be 7(2*128)6/7=$811.53. Since this is less than the cost with the new technology,
you would not be willing to pay to lease the new technology.
Another technology which is available is f(L,K)=8L+4K. What would your marginal
cost equation be if you adopt this technology? (5 points)
With linear production you will either use only L or only K. Comparing MPl/w=8/12
with MPk/v=4/4, we see that the firm will use only K (L=0). TO make q units the firm
will buy k=q/4. The cost is wL+vK=0+48q/4=q. MC=dTC/dq=1.
Q2. (30 points) You are the head of a labor union in the textile industry. A typical firm
in this industry has production given by f(L,K)= L1/2K1/2. The rental rate of capital is
v=25. Currently, every firm in this industry has to hire exactly 25 workers at a wage rate
of 10. Plot the isocost and isoquant curves for a firm making a) 15 units and b) 20 units.
(5 points. You should have 1 graph with all four curves)
The figure is similar to the one on page 322 in the text except that we are holding labor
fixed.
Assuming that this is a competitive industry with 5 firms, what will be the equation for
the market supply curve? (8 points)
Since L=25 we know that q= 5K1/2 or K=q2/25. TC=wL+vK=10*25+25*q2/25
=250+q2. So MC=2q. Since MR=MC and P=MR for a competitive firm the firm’s
supply curve is P=2q. With 5 firms we add the quantities that each firm will produce so
we have P/2+P/2+P/2+P/2+P/2=5P/2. The market supply curve is Q=5P/2 or P=2Q/5.
Suppose that demand is given by P=70-Q. How many units will the typical firm produce
and what profits will it earn? (6 points)
Setting supply equal to demand we have 2Q/5=70-Q or 7Q/5=70 or Q=50. Since the
market quantity is 50 each firm makes 10 units. The price will be 20 (found by plugging
the market quantity into demand or market supply). The firms profits will be 20*10-250102 = -150. Notice that this profit is greater than -250, which is what the firm would
loose if it shut down.
As the union boss, you are considering demanding that the wage rate increase. How will
this impact the typical firm? How will it impact the market? (3 points each)
This will increase the fixed cost and the total cost, but it will not impact MC. Since MC is
the same, market supply is unchanged. Ultimately, this will cause more firms to leave the
market as profits are lower.
An alternative that you are considering is to force each firm to hire more workers. How
will this impact the typical firm? (5 points)
Increasing the number of workers will increase fixed cost, but it will also change the
amount of capital the firm has to hire to make any level of output. With more labor, less
capital will be needed (we have moved down and to the right on the isoquant curves) and
thus MC will fall. With the lower MC curves, market supply is shifted to the right
lowering the market price.
Q3. (40 points) You are the owner of a company that makes Hog Hoop Hats. Your total
costs are given by TC=q2+5q+40. Find AFC and AVC. (6 points)
FC equal TC when q=0. So FC=0+0+40=40. AFC=40/q. VC=TC-FC= q2+5q.
AVC=VC/q=q+5.
If the market for Hog Hoop Hats is competitive with a price of 15, how many units
should this firm produce? (4 points)
The competitive firm sets MC=P (P=MR for a competitive firm). MC=dTC/dq=2q+5.
So we have 2q+5=15 or q=5.
What is the shutdown price for this firm? (4 points)
The shutdown price is where AVC and MC cross. So we set q+5=2q+5 and we get q=0.
For this quantity we see that MC=0+5=5, so the shutdown price is 5.
Suppose that the University awards you the exclusive right to produce Hog Hoop Hats, so
that you are a monopolist. What price should you charge and what profit will you earn if
demand is 101-Q? (5 points each) Sketch a graph of this monopolist, clearly labeling the
appropriate curves and the profit. (5 points)
The monopolist sets MR=MC. In this case MR=101-2Q (TR=101Q-Q2). So we have
101-2q=2q+5 or 4q=96 or q=24. To demand curve tells us that people are willing to
pay 101-24=77 for 24 units. So the price the monopolist should charge is 77. The profits
would be 77*24- (24)2-5(24)-40=$1112.
Explain why a firm never wants to operate along the inelastic portion of the demand
curve. (3 points)
If demand is inelastic then raising the price and lowering the quantity will increase total
revenue. At the same time, lowering quantity will lower costs, so profits which are TRTC could be increased by decreasing output if the firm was operating along an inelastic
portion of the demand curve.
What is the deadweight loss due to the exclusive agreement? (5 points)
First we need to determine the efficient quantity, which is where P=MC or 101-q=2q+5.
This gives 3q=96 or q=32. We also need to determine the MC of the last unit the
monopolist actually produces (this gives the height of the DWL triangle).
MC=2q+5=2(24)+5=53. Therefore DWL=.5*(77-53)*(32-24)=$96.
If you could perfectly price discriminate what would be the deadweight loss? (3 points)
Since every buyer pays what the good is worth, the firm will make the efficient quantity
and DWL=0.