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課程名稱︰個體經濟學二
課程性質︰必修
課程教師︰江淳芳
開課學院：社會科學院
開課系所︰經濟系
考試日期（年月日）︰
考試時限（分鐘）：
試題 :
2010 個體下學期期末考 江淳芳
選擇題不需要計算過程，計算題請詳答。Good Luck!
選擇題 (15%)
1. There are two types of used cars, high quality and low quality. Buyers
cannot distinguish the two types until after they have purchased them. Owners
of high-quality cars will sell them if the price is $2,000 or higher. Owners of
low-quality cars will sell them if the price is $1,000 or higher. Buyers value
a high-quality used car at $3,466 and a low-quality used car at $1,200. Suppose
that 30% of used cars are of high-quality and 70% of used cars are of
low-quality. In equilibrium,
(a) All used cars will be sold.
(b) Only low-quality used cars will be sold.
(c) No used cars will be sold.
(d) Onlt high-quality used cars will be sold.
(e) High-quality used cars will sell for a uniforly higher price than
low-quality used cars
2. In the game matrix below, the first payoff in each pair goes to player A who
chooses the row, and the second payoff goes to player B, who choose the column.
Let a,b,c, and d be positive constants.
Player B
Left Right
┌───┬───┐
Player A Top │a,1 │b,1 │
├───┼───┤
Bottom│1,c │1,d │
└───┴───┘
If player A choose Bottom and player B choose Right in a Nash equilibrium, then
we know that
(a) b>1 and d<1
(b) c<1 and b<1
(c) b<1 and c<d
(d) b<c and d<1
(e) a<1 and b<d
3. Tip can write 2 pages of term paper or solve 2 workbook problems in an hour,
while Spot can write 2 pages of term paper or solve 6 workbook problems in an
hour. If they each decide to work a total of 8 hours and to share their output,
then if they produce as many pages of term paper as possible given that they
produce 14 workbook problems,
(a) Tip will spend all of his time writing term papers and Spot will spend some
time at each task.
(b) Spot will spend all of his time writing term papers and Tip will spend some
time at each task.
(c) Spot will write term papers only and Tip will do workbook problems only.
(d) Both students will spend some time at each task.
(e) Tip will write ter, papers only and Spot will do workbook problems only.
計算題 (85%)
1. (20%) Two players are engaged in a game of "chicken". There are two possible
strategies, Swerve and Drive Straight. A player who choose to Swerve is called
"chicken" and gets a payoff of zero, regardless of what the other player does.
A player who choose to Drive Straight gets a payoff of 84 if the other player
Swerves and a payoff of -36 if the other player also choose to Drive Straight.
(a) Please write down a payoff matrix for this game.
(b) Please find all pure strategy Nash equilibria for this game.
(c) Please find the mixed strategy Nash equilibria for this game.
2. (20%) Xavier and Yvette are the only two persons on a desert island. There
are only two goodsn nuts and berries. Xavier's utility function is
U(N_x,B_x) = N_xB_x. Yvette's utility function is U(N_y,B_y) = 5N_y + B_y.
Xavier is endowed with 4 units of berries and 13 units of nuts. Yvette is
endowed with 6 units of berries and 8 units of nuts.
(a) Draw and Edgeworth box with nuts on the horizontal axis, showing the
initial allocation and sketching in a few indifference curves. Measure Xavier's
consumption from the lower left. And please show where the Pareto optimal
allocations are.
(b) In the competitive equilibrium for this economy, what is the price ratio of
berry and nut (price of berry/price off nut)?
(c) How many units of berries does Xavier consume at the competitive
equilibrium?
3. (25%) Consider a simple model of continuous public goods with two
individuals. Each individual has an income of $30 and preferences over a public
good (G) and a private good (individual 1 consumes z_1 and individual two
consumes z_2). Prices of both the private and public goods equal $1.
Assume that individuals have equally-weighted Cobb-Douglas preferences over the
public and private goods:
U_1 = (1/2)ln(G) + (1/2)ln(z_1)
U_2 = (1/2)ln(G) + (1/2)ln(z_2)
(a) (8%) Using these preferences, write an expression for the Pareto efficient
provision. Using this expression and the social resource constraint
(z_1 + z_2 = 30 + 30 -G), solve for the Pareto-efficient provision of public
goods (G^E). Your final answer should be a number.
(b) (7%) Assume now that public goods are funded through private contributions
(g_1,g_2). In this case, G = g_1 + g_2 and z_1 = 30 - g_1 (with a similar
expression for individual 2). Find the best-response function g_1(g_2) for
individual 1.
(c) (5%) Using your answer in part (b), solve for the symmetric Nash
equilibrium contrivution level (g^N).
(d) (5%) How does the private provision of public goods gn compare to the
Pareto-efficient provision level (G^E)? Interpret any differences.
4. (20%) All 1,001 residents of Boston love to drive their cars and , as a
consquence, the roads are choked with congestion. Residents have identical
preferences, and the utility function of a typical driver is
U(x,d,c) = x + 16d - d^2 - 6c/1000, where x is the citizen's private
consumption, d is the hours spent driving, and c is the total hours spent
driving by the other citizens of Boston. Assume that the price of the private
good (x) equals 1. and each citizen is endowed with income of $40. In the
absence of taxes, there are no costs associated with driving.
(a) Assuming that driving is totally unregulated and that drivers do not
internalize the congestion extermality, how many hours will each resident
drive? What is the congestion (c) that each resident face?
(b) What is the Pareto efficient level of driving (d) and congestion (c)?
(c) Suggest a unit tax on driving to correct this market failure.
(Hint: Each resident has to pay t˙d to the government when driving d hours.)
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