中级微观经济学期末试题

09级中级微观经济学期末试题
1.Suppose the airlines fares are reduced by 50% after one flies 25,000 miles a year. Show that
the preferential price will NOT affect a typical flyer-customer with well-behaved preferences.
(Graphing is enough) (10 points)
2.Depict the income effect and substitution effect of a non-Giffen inferior good under SLutscky
decomposition. (10 points)
3.Suppose in the market of some commodity, the supply curve is P=Q+20, the (inverse) demand
curve is P=50-Q/3. Roughly graph and (accurately) calculate to
a.Determine the equilibrium.(5 points)
b.Determine the new equilibrium if an export demand P=50-Q/2 is added. (5 points)
4.Draw a typical edgeworth box showing very clearly how to determine the final monopolistic
equilibrium when one of the two agents behaves as a monopolist. Please also indicate in the graph that the final allocation is Pareto inefficient.
5.Smith is the owner of a sole mineral water spring in an isolated economy. It costs Smith $2
per gallon to get his water bottled. The inverse demand curve for Smith’s water is P=20-Q/5, where p is the price per gallon and q is the number of gallon sold.
a.Write down an expression π(q) for profits as a function of q. find the profit-maximizing
choice of q for Smith, and the corresponding price and profit. (5 points)
b.Suppose now Henry, Smith’s neighbor, finds also a mineral spring that produces mineral
water just as good as Smith’s, but it cost Henry $6 a bottle. The total market demand remains as before. Suppose that Smith is the leader and Henry is the follower, please determine the Stackberg leadership equilibrium.
6. A monopolist can sell outputs Q1 and Q2 in two markets that are effectively isolated from one
another. His cost function is C=1988+29Q+Q2/40, where Q=Q1+Q2. The demand in the two markets are given by Q1=480-4P1 and Q2=200-2P2 respectively. Graph to show roughly your solution to the following 2 questions:
a.How much does he sells in each market? Compare the prices and the price elasticities of
demand in the 2 markets. (10 points)
b.If the markets are not separated any more and he must charge the same price in the two
markets, what price does he charge? How much does he sell in each market? (10 points)
c.Calculate the profit change from case a) to case b). (5 points)
7.John Henry, an avid gardener, has found that the number of happy plants, h, depends on the
amount of light, l, and water, w. the production function is as follows: h=min﹛4l, w﹜.
Assume that each unit of light costs $1 and each unit of water costs $2. Suppose John wants to produce 10 happy plants at the minimum cost.
a.What are the amounts of light and water required？（5 points）
b.How much does John have to pay for? (5 points)
c.Derive Henry’s cost function. (5 points)
8.Player 1 and 2 are bargaining over how to split one dollar. Both players simultaneously name
shares they would like to have, s1 and s2, where 0 ≤s1,s2≤1. If s1+s2≤1, then the players receive the shares the named; if s1+s2>1, then both players receive 0. What are the pure-strategy Nash equilibrium of this game? (10 points)
Answer:
1、
2、图略。

注意是non-giffen。

即SE和IE的方向相反，|SE|>|IE|
3、a P= 45/2，Q=85/2
b P=45 Q=25 (两个小问都要画图)
4、图略（B的提供曲线，A、B的无差异曲线，预算约束线or relative price，效率损失的区域）
5、a q*=45,p*=11, π*=405
b q H =(70-q S)/2, q S =55 q H=7.5
6、a Q1*=160，Q2*=60，p1*=80,p2*=70, ε1= -2,ε2= -7/3
b Q1*=520/3, Q2*=140/3
c πa=22266/3, πb=21866/3
7、a l*=2.5, w*=10
b 22.5
c 2.25h
8、all pairs satisfy s1*+s2*=1。