MICROECONOMICS - second partial test
Full name:
N° ‘matricola’:
- Time: 50 minutes.
- For type A questions (open) use only the delimited space available. Every type B question (multiple choice) has one
and only one correct answer. Any Answer not justified by calculations, graphs or whatever, will not be considered.
Use only the present sheet for calculations, graphs and any other observation.
1a. A's wealth is W1 = 100 if state 1occurs, W2 = 400, if state 2 occurs. States 1 and 2 occur with
probability π1 = ¾ and π2 = ¼, respectively. A's preferences for non contingent consumption c are
represented by the utility function UA = c1/2 . A's preference for contingent consumption satisfies the
expected utility property. Define A's marginal rate of substitution, between consumption in state 1 and 2.
1b. A's initial wealth is zero. His utility function for non contingent consumption is UA = 4c1/2. A's
preference for contingent consumption satisfies the expected utility property. A is offered the lottery L,
paying the prize L1 = 9 with probability 2/3, and the prize L2 = 81 with probability 1/3. Determine the risk
premium that the consumer assigns to the lottery L.
a) 0
b) 4
c) 8
d) 2
e) − 2
f) no answer
2a. Define and discuss the concept of adverse selection.
2b. Worker’s expertise is unobservable when worker and firm sign a labor contract. Firms accept a
document certifying attendance of h hours training per week as a quality signal, and offer a weekly
wage of 1500 euro to certificate holders, and a weekly wage of 1000 euro to any worker without the
training certificate. Workers living in the region are of two types, skilled (A) and unskilled (B).
Worker's preferences for wage W and education hours h are represented by the utility function
Ui = W − hCi , where i is worker type (i = A, B), CA = 25 and CB = 50. Evaluate which, among the
following values of h, is consistent with a ‘separating equilibrium’ with signaling.
a. 4
b. 6
c. 12
d. 22
is. None of the other answers
3a. A and B have identical initial wealth W. Following an agreement to share lottery L prizes, A's wealth is
W1A , if state 1 occurs and W2A if state 2 occurs; B's wealth is W1B if state 1 occurs, and W2B if state 2
occurs. States 1 and 2 occur with probability 1/3 and 2/3, respectively. Knowing that A is risk-neutral, and
that B is risk averse, what is the condition ensuring that risk-sharing between A and B is Pareto efficient?
3b. There is a probability p = ¼ that agent's A wealth W = 2000 suffers a damage D = 2000. Agent A can
ensure wealth K, 0 ≤ K ≤ W, paying an insurance premium γK , where the premium per unit of money
fixed by the insurance company is γ = ½. A's utility for non-contingent consumption is UA = 2c1/2. A's
preferences for contingent consumption satisfy the expected utility property. What is the amount of
insurance K chosen by A?
a) 2000
b) 400
c) 500
d) 200
e) none of the other answers
4a. Define and discuss the concept of 'monopolistic competition' and specify the conditions of long-run
equilibrium in this type of industry.
4b. A firm has production function y = x11/2x21/2. Factor prices are w1 = 9, w2 = 1, respectively. The
minimum total cost to produce y = 120 is:
a) 240
b) 460
c) 720
d) 680
e) none of the other answers is correct
5.a Define and discuss the concept of pre-contractual opportunism in the insurance field
5.b In a competitive industry firms have identical cost function:
c(0) = 0; c(y) = 16 + 4y2 for y > 0. Determine the long term price p in this industry, and the number n of
firms in the market, assuming that market demand is Yd = 216 − p.
a) p = 8
n = 200
b) p = 12
n = 160
c) p = 14
n = 120
d) p = 16
n = 100
e) none of the other answers is correct
Answer to type b questions
1.b
2.b
3.b
4.b
5.b
8
c
400
720
d
MICROECONOMICS - second partial test
Full name:
N° ‘matricola’:
- Time: 50 minutes.
- For type A questions (open) use only the delimited space available. Every type B question (multiple choice) has one
and only one correct answer. Any Answer not justified by calculations, graphs or whatever, will not be considered.
Use only the present sheet for calculations, graphs and any other observation.
1a. Define and graphically represent the notion of consumer’s risk aversion, assuming that the preferences
for contingent consumption satisfy the expected utility property
1b. The wealth of consumers A and B is 200 Euro. Their utility functions for non contingent consumption
are UA = c1/2, UB = c, respectively. A's and B's preference for contingent consumption meets the expected
utility property. A is offered a lottery L, yielding a negative prize -100 euro, if state 1 occurs, and a
positive prize 700 euro, if state 2 occurs. The probabilities of state 1 and 2 are 4/5 and 1/5, respectively.
Agent A rationally decides she does not want to bear the full risk of L. She decides to sell the lottery L to B.
In return, B will pay her 20 Euro, if state 2 occurs, and x euro, if state 1 occurs. What is the value of x, that
makes the risk allocation Pareto efficient ?
a) 0
b) 10
c) 20
d) 40
e) none of the other answers
2a. Define and discuss the concept of separating equilibrium through signaling
2b. In a Cournot duopoly, firms 1 and 2 produce, respectively, y1 and y2. They have identical total cost
function C(yi) = 2 yi, i = 1, 2. Market demand function is y = 20 - p, where y = y1 + y2. The market price p in
a Cournot equilibrium is:
a. 10
b. 8
c. 6
d. 16
e. None of the other answers
3a. Define and illustrate with examples the concept of post-contractual opportunism in the insurance field.
3b. There is a probability p = 1/5 that agent A wealth WA = 10000 suffers a damage D = 5000. A can ensure
wealth K ≤ D, paying a premium γK, where the premium γ per unit of insurance, fixed by insurance
company, is 'fair'. A's utility function for non contingent consumption is UA = 2c1/2. A's preference for
contingent consumption satisfies the expected utility's property. What is the optimal value K of insurance
agreed upon by A?
a. K = 1000
b. K = 2000
c. K = 3500
d. K = 4500
is. K = 5000
4a. Define and discuss the concept of technical rate of factor substitution (TRS), and specify its use in
solving a problem cost minimization for a competitive firm
4b. A's initial wealth is zero. His utility function for non contingent consumption is UA = 4c1/2. A's preference
for contingent consumption satisfies the expected utility property. Consumer A is offered the choice
between a sure money prize x and the lottery L, paying the prize L1 = 16, with probability ¼, and the prize
L2 = 64, with probability 3/4.
a) A accepts the sum x if x < 64
b) A accepts the sum x if x > 30
c) A accepts the sum x if x < 30
d) A accepts the sum x if x > 49
e) A accepts the sum x if x < 49
f) no answer
5.a Specify and discuss the conditions defining a long-run equilibrium of a perfectly competitive industry.
5b. A firm produces output q with a technology represented by the production function q = f (x, y) = 2x + y.
If the unit prices (in euro) of the factors x and y are, respectively, px = 1 and py = 1, then the minimum cost to
produce q = 200 is C (200) = :
a. 50
b. 200
c. 100
d. 150
e. none of the other answers
Answer to Type b questions
1b
2.b
3.b
4.b
5.b
20
8
5000
d
100
MICROECONOYCS - Questions for second partial test
1. A farm producing almonds M and one producing honey H operate in neighboring fields, giving rise to
positive external effects in production. In particular, each producer's output exerts external effects on the
other's cost. M has cost function Cm (m, h) = 24m + m2 ─ 12h. H has a cost function Ch (m, h) = 16h + h2 ─
8m, where m and h indicate the amount of almonds (m) and honey (h) respectively. The market prices of
honey and almonds are given and constant: pm = 48, ph = 24. Determine the Pareto efficient productions of m
and h.
2. There is a probability p = 1/5 that agent's A wealth W = 40000 suffers a damage D = 20000. Paying a
premium γK to an insurance company, where γ = ¼, agent A can ensure wealth K ≤ D. A’s utility function
for non contingent consumption is UA (c) = log c. A's preference for contingent consumption satisfies the
expected utility property. If Cb and Cg indicate A's consumption, if damage occurs, and does not occur,
determine A’s choice of K, Cb and Cg.
3. Worker’s expertise is unobservable when worker and firm sign a labor contract. The firms in a
region decide to accept attendance to a training course of h weekly hours as a quality signal. On this
ground, they offer a weekly wage 1200 euro to trained workers, and 900 euro to untrained workers.
Workers living in the region are of two types, skilled (A) and unskilled (B). The preferences of a
type i worker, for wage W and education hours h, are represented by the utility function Ui = W −
hCi where CA = 20 e CB = 50. Determine the interval of h, that is consistent with a separating
equilibrium through signaling.
4. The initial wealth of consumers A and B is WA = WB = 0. They have identical utility function for
non contingent wealth UA (W) = UB (W) = log W. A and B decide to share the prizes L1 = 120 and
L2 = 20 of a lottery, according to the scheme: L1A + L1B = L1 ; L2A + L2B = L2. The prizes L1 and
L2 occur with probability ¼ and ¾, respectively. Knowing that L2B = 5, what is the value L1A that
makes the risk allocation between A and B Pareto efficient?
5. Define and discuss the notion of ‘cost function’. Specify the behavior of the long-run average cost
(LAC) and the long-run marginal cost (LMC) of a firm with production function y = x11/3 x21/3
6. In the market for second-hand cars there is a fraction π of high quality cars, and a fraction (1- π)
of low-quality cars. Buyers are not able to observe the quality of the cars and there is no way to
certify it. Buyers are willing to pay up to 12.000 euro for a good-quality car of and up to 6000 for a
bad-quality one. Sellers are willing to offer a good quality car at a minimum supply price 10.000
euro, and a bad quality car at a minimum price 5000 euro. What is the range of π producing adverse
selection in the second-hand car market?
a) π < 5/6
b) π ≥ 2/3
c) π < 3/4
d) π < 2/3
e) π ≥ 3/4
f) none of the other answers is correct
7. In a competitive industry firms have identical cost function:
c(0) = 0; c(y) = 400 + y2 , if y > 0. Indicate the long term price p in this industry, and the number n
of firms in the market, assuming that market demand is Yd = 840 - p.
8. In a duopoly, firms 1 and 2, produce, respectively, y1 and y2. They have identical total cost
function C(yi) = 4 yi, i = 1, 2. The market demand function is y = 360 - p, where y = y1 + y2 .
Determine the market prices in a Cournot equilibrium and in a Stackelberg equilibrium, with
quantity leadership.
9. Characterize the pay-off matrices of a "prisoner's dilemma" type game, and of a noncooperative game, with two Pareto rankable Nash equilibria.
10. A's initial wealth is zero. His utility function for non contingent consumption is UA = c1/2. A's
preference for contingent consumption satisfies the expected utility property. A is offered the lottery
L, paying prize L1 = 16 with probability ¾, and prize L2 = 6400 with probability 1/4. Determine
the risk premium that consumer A assigns to the lottery L.