The Bologna Center of The Johns Hopkins University
MICROECONOMICS
(Professors M. Alvisi and E. Carbonara)
Mid-Term Exam
8/11/2012
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You have 2 hours to complete this exam.
Total points available: 100.
Plan your responses carefully, as points are awarded for correct, complete and
exhaustive answers.
Provide your answers on the blue book that has been given to you. You are allowed to
use ONLY 1 BLUE BOOK FOR THE ENTIRE EXAM.
DO NOT FORGET TO SIGN THE HONOR CODE ON THE OTHER SIDE OF
THIS SHEET AND TO HAND IT BACK TOGETHER WITH YOUR BLUE BOOK
AT THE END OF THE EXAM.
Part A. Short (Technical) Questions (24 points – 6 points each).
Please, answer FOUR of the following SIX short questions:
1) Why, in a perfectly competitive equilibrium, is price in the long run always equal to minimum
average cost? Is this violating the profit maximization rule, requiring p=MC?
2) Might a consumer choose an optimal consumption bundle such that her marginal rate of
substitution does NOT equal the price ratio? Explain briefly.
3) When the gym monthly subscription increases, Tom spends a smaller percentage of his income,
which is fixed, on gym than he did before. Is Tom’s demand for gym price elastic or inelastic?
Briefly Explain.
4) What is the economic meaning of the assumption of convex isoquants? What would be the
implication of having concave isoquants?
5) What is the meaning of the transitivity axiom in consumer theory? Why would the consumer
model collapse without it?
6) What causes the marginal cost curve to eventually rise in the short run? In the long run?
Part B. Theory Questions (30 points – 15 points each)
Please answer TWO of the following THREE questions:
1) The average price of an apartment in Geneva rose more than 12% last year but the number of
apartment sales fell nearly 5%. A realtor informs you that there has been growing demand for
housing in Geneva because of the influx of international civil servants. Draw a diagram of the
market for apartments in Geneva to illustrate the case of a shift in demand and/or supply curves that
is consistent with the observed changes in prices and quantities. Does the information provided by
the realtor fully explain the observed data?
2) The Consumer Price Index for a single good is computed using the formula
𝑢𝑝𝑑𝑎𝑡𝑒𝑑 𝑐𝑜𝑠𝑡
𝐶𝑃𝐼 = 𝑏𝑎𝑠𝑒 𝑝𝑒𝑟𝑖𝑜𝑑 𝑐𝑜𝑠𝑡 × 100. The “updated cost” is the price of a good in a given year (i.e., the
price of the good in 2012), the “base-period cost” is the price of the good in some reference year
(e.g., in the year 2000). Consider the CPI for gasoline. The base year is 2005: in that year the price
of gasoline was pG2005=$2 per gallon. The 2008 CPI for gasoline is 200.
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a) Consider a family with an income I=$1200, that in 2005 was spending $400 in gasoline
and $800 in all other goods. Assuming that the family’s income has not changed and that also the
prices of all other goods have remained the same, compute how much the family would spend to
buy exactly the same bundle it was buying in 2005 at 2008 prices.
b) The US Government is willing to compensate families for the increase in gasoline prices.
The initial suggestion is to provide each family with an income subsidy exactly equal to the increase
in expenditure from 2005 to 2008. With the help of a qualitative diagram, carefully sketch the
effects of such policy on consumption of gasoline and all the other goods. Would this policy be
effective in restoring the family’s purchasing power? Explain.
c) Explain, both graphically and in words, why using a compensating variation method
might be preferable for the government to compute the subsidy.
3) Suppose that the market in Bologna for taxicab rides is perfectly competitive. You observe that
the number of taxicabs is growing.
a) Draw two diagrams side by side. In the diagram on the left, draw the demand for rides of an
individual taxicab (its “firm-specific” demand curve), its long-run marginal cost curve, and its longrun average cost curve. In the diagram on the right, draw the market demand and supply curves of
taxicab rides.
b) Why is the number of taxicabs growing? Explain using your diagrams.
c) How will the growing number of taxicabs change the market price of taxicab rides, the individual
taxicab’s profit-maximizing output, and the individual taxicab’s long-run average cost? Explain
using your diagrams.
Part C. Exercises (46 points)
Please solve TWO of the following THREE exercises.
1. A market consists of two different groups of consumers: loyal customers (type A) who have an
aggregate demand equal to QA=14 -P, and occasional customers (type B), whose aggregate
demand is QB=16 - 2P. Total supply to both types of consumers is given by QS=5 +2P.
a) Determine total demand in the market algebraically, for every possible level of the price.
Draw demand schedules for both groups A and B in a graph. In the same graph, draw
total aggregated demand. (6 points)
b) Determine the equilibrium price and quantity in the market. What part of total quantity is
purchased by loyal customers? What part by occasional customers? (4 points)
c) Compute the price elasticity of total demand and supply in equilibrium. Determine also
the price elasticity for each market group. (4 points)
d) Compute consumer surplus in both market segments and aggregate consumer surplus. (4
points)
e) A shock hits supply. The National Bureau of Statistics collects the following information
about price/quantity pairs characterizing the new supply pattern:
P Q
1 9
2 12
3 15
4 18
Based on the data provided, estimate the new supply function and compute the new
equilibrium. Which type of shock could have generated the new supply function?
Explain. (4 points)
f) (BONUS) Compute the price elasticity of demand at the new (approximated)
equilibrium. Is it higher or lower than its initial value? Explain why this is the case. (4
points)
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2. Suppose that engineers have estimated that the production function for a steel firm is of the
form: Y = K 0.2 L0.8 (MRTS=4K/L). Capital (K) and labor (L) are the only two inputs and both
are variable. The firm’s cost of labor (w) is equal to $8 while the cost of capital (r) is equal to
$2.
a) What type of production function is this? Provide an economic definition for the
marginal rate of technical substitution, explaining (from an intuitive point of view) why
it is equal to the ratio of the marginal productivities. (3 points)
b) Provide a definition of the concept of returns to scale. What kind of returns to scale
characterizes this production function? Explain. (5 points)
c) Compute the firm’s optimal choice of factor inputs when its target is an output level
equal to Q = 10. (6 points)
d) What is the total budget needed to produce Q = 10 at the given input prices? (3 points)
e) How much would the firm produce in equilibrium if it were given a budget equal to 100?
Do you need any calculations to answer this question? Explain. (6 points – CAREFUL:
most of the credit for question 2.e) is given by the explanation. A number for Q and a
Y/N answer would yield 1 point only)
f) (BONUS) What are the firm’s total costs of producing a generic quantity Q? In other
words, what is its total cost function? What are the firm’s average and marginal cost
functions? (4 points)
3. In a perfectly competitive market, in the short run, N=5 firms produce using a technology
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characterised by the following total cost function 𝑇𝐶 = 10 + 2 𝑞 2 + 10𝑞 (marginal costs are
equal to MC=q+10). Marked demand is given by QD = 100 – 5P.
a) Determine the individual supply function for each firm in this market. (Careful:
remember that the individual supply function consists of both an expression for quantity
supplied as a function of the price and of a “feasibility condition”, i.e., a minimum price
below which no production occurs in the short run). (4 points)
b) Determine the aggregate supply function in this market. (4 points)
c) What is the equilibrium price and quantity in the market? (3 points)
d) Do individual firms make positive or negative profits at the equilibrium price? Are they
willing to produce a positive quantity? Why or why not? (5 points, of which, 2 for the
explanation)
e) How would you expect the number of firms in this market to change in the long run?
Why? (3 points)
f) Compute total industry profits and aggregate producer surplus in the equilibrium. Can
you see a relationship between producer surplus and total profits? (4 points)
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g) (BONUS) Consider now the long-run. Total costs are now given by 𝑇𝐶 = 2 + 2 𝑞 2 +
10𝑞 (there is still a fixed component in the TC function. This is done to guarantee the
desired U-shape to the AC. Alternatively, we could use a cubic function, but algebra
would then be cumbersome). Find the quantity produced by each firm, the price at which
such quantity is sold in the market and the number of firms operating in the market in
the long-run equilibrium. (4 points)
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