ECON 201 (Fall 2015)
Department of Economics, SFU
Prof. Christoph Lülfesmann
Final Exam
Please solve ALL of the problems below.
I. Short Problems - Explain! No credit will be given without a justification of
your answer. (8 pts each)
1. A firm is described by a cost function for which marginal costs are (everywhere)
increasing in output y. For some output price p, graph the firm’s producer surplus in two
different ways (and in two different diagrams). Explain in words why both methods work.
2. Amanda consumes blue (good 1) and red (good 2) pencils. Initially, each of these
goods costs 1 dollar but for some unknown reason, the price of blue pencils doubles to 2
dollars. Does the price increase make Amanda worse off when her preferences are described
as (a) U = min{x1 , 2x2 }, (b) U = 3x1 + 2x2 , or (c) U = x1 + x2 ? Argue carefully!
3. What is the ”Law of Diminishing Marginal Product”? What is a ”Constant Returns
to Scale (CRS)” technology? Can the ”Law” apply to CRS production functions? Why or
why not? Explain carefully!
4. Mike tries to impress his new girlfriend Kathryn: ’In a market with perfect competition, firms are unable to make any profits’. Should Kathryn be impressed? Explain
carefully whether or not (or under which circumstances) Mike’s belief is correct/incorrect.
5. An industry consists of N = 10 firms, each with a cost function C(y) = 20y + y 2 .
The (inverse) industry demand function is P D (Q) = 100−(4/5)Q. (a) Compute and graph
the market equilibrium in this industry (label everything). (b) Suppose the government
imposes a sales tax of t = 20 dollars per unit of consumption. Compute and graph the
new equilibrium (p∗d , p∗s , Q∗ )! (c) Compute and graph the deadweight loss of the tax.
6. (Bonus Question) Graph the Engel curves of both goods for the case of quasilinear
preferences (label everything). Explain your results in words, using a graph with M U1
respectively M U2 on the vertical axis, and x1 respectively x2 on the horizontal axis.
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II. Long Problems
Long Problem 1 (30 pts.) (Explain your answers!)
Tom has preferences over fitness classes (good 1) and action movies (good 2), which he
consumes in quantities x1 and x2 , respectively. His preferences are described by the utility
function
3/2
U (x1 , x2 ) = x1 x2 .
Tom’s income is m = 120, and unit prices are p1 = 4 and p2 = 2.
a) (i) Find Tom’s demand function for fitness classes, good 1. Explain your procedure,
and describe the main characteristics of the demand function in words. (ii) Which
consumption bundle (x∗1 , x∗2 ) will Tom choose for the given market prices? Compute
and graph his optimal choice (label everything), and explain briefly.
b) The government wants to raise R = 8 dollars in tax revenues from Tom through an
ad valorem sales tax on good 1. Which tax percentage t∗ achieves this goal? Explain
your computations, please.
c) [ignore b)] Tom finds out that on some days, his beloved action movies cost only
p2 = 1. Also, a fitness studio offers tryouts where the first 10 fitness classes are free.
(i) Graph Tom’s new budget constraint in this situation (label everything, and give
slopes). (ii) Find the mathematical formula for his budget constraint (be precise).
(iii) Compute and graph (you can use the graph in (i)) his new optimal consumption
choice.
d) [ignore b) and c)] Tom spots the following ad. (i) His favorite fitness clubs PIPES
offers basic memberships (which include 40 visits/month) for just 84 dollars. Should
Tom become a member, or not? (ii) Tom realizes that as an econ student, he doesn’t
have time to consume more than a combined total of 42 fitness classes and/or action
movies per month (assume the time requirement for movies and fitness classes is the
same). How many fitness classes and action movies will he consume, if he chooses to
become a member? Should he still accept the membership offer? Explain your steps
precisely.
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Long Problem 2 (30 pts.) (Explain your answers!)
Firm A produces output using the production function
y = (3/4)K 1/2 L.
The firm pays r = 2 dollars per unit of capital K, and w = 24 dollars per unit of labor.
a) Which input combination should firm A use to produce y = 1 unit of output in a
cost minimizing way? Compute the solution (K ∗ , L∗ ). Then, graph your solution
using the concept of isoquants and isocost lines (label everything). What are the
firm’ production costs C(1) for one unit of output?
b) In the short run, firm A’s labor input is fixed at L̄ = 10. Compute the profit
maximizing amount of capital K ∗ (L̄) when the firm faces an output price of p = 16.
How large are the firm’s short run profits? Illustrate the firm’s optimal capital input
(and output) choice, using a graph that shows iso-profit lines (label everything).
c) Again, assume firm A’s labor is fixed at L̄ = 10. Compute the firm’s short run cost
function C(y). Is there an easy way to find the firm’s long run cost function where
both factors are variable? Argue precisely why or why not (for this last question, no
computations are necessary).
d) Consider firm B which operates in the same market and faces the same prices as firm
A. However, firm B’s production function is y = (3/4)min{6L, K}. For the given
input prices (w = 24, r = 2), what do firm A and firm B have in common? Would
this feature change if input prices changed? What is firm B’s long run cost function?
Explain!
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