推 TINTINH :已收精華區:) 04/19 23:24
課程名稱︰個體經濟學二
課程性質︰必修
課程教師︰古慧雯
開課學院：經濟系
開課系所︰社會科學院
考試日期（年月日）︰99.04.19
考試時限（分鐘）：13:30-15:10(延至15:15) (100+5mins)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
31 points in total. You have to state your reasoning clearly. No point will be
given to an unexplained answer.
1.Monopolist A faces an inverse market demend of p=f(q), where q and p denote
the quantity and the price. His marginal cost function is MC1(q).
(a)(1 pts.)Please derive his marginal revenue function to be
MR1(q)=f(q)+f'(q)q.
(b)(2 pts.)A's customers now have to pay a sales tax of $t per unit. Please
derive A's new marginal revenue function MR2(q) in terms of MR1(q).
(c)(2 pts.)What happens if instead of taxing customers, A has to pay an
excise tax of $t per unit? Please derive A's new marginal cost function
MC2(q) in terms of MC1(q).
(d)(2 pts.)Please compare A's output when a sales tax is imposed and when an
excise tax is imposed.
2.Monopolist B has two markets with demend functions: qa=100-pa, qb=80-pb,
where qi and pi denote the quantity and price in market i, i=a,b. B considers
the third-degree discrimination. B has a marginal cost function MC(q)=q.
(a)(4 pts.)It is known that B distributes his outputs q in two markets in
such a way that his total revenue could be maximized. Let MR(q) denote B's
marginal revenue function. Please calculate MR(5) and MR(50)
(b)(2 pts.)How many units will B produce to maximize total profit?
3.(4 pts.)A club has 3 members: A, B and C. They'll vote to decide whether to
admit a new member (D or E) to the club. the voting procedure is as follows.
They'll first vote to decide to discuss the case of D or the case of E. If
the majority favors to discuss the case of D(E), they'll then vote to decide
whether to admit D(E) or nobody.The preferences are known to be:
A:D > nobody > E
B:nobody > D > E
C:E > D > nobody
In a subgame perfect equilibrium, how will B vote in the first round?
4.In the following game, the row player has pure strategies s1 and s2 and the
column player has pure strategies t1, t2 and t3. The first(second) element
in the payoff vector denotes the payoff to the row(column) player.
│ t1 t2 t3
─┼──────
s1│1,0 9,4 0,9
s2│4,7 7,3 3,0
(a)(1 pts.)Does the column player have a pure dominant strategy?
(b)(2 pts.)Examine the space of the mixed strategies. Does the column player
have a pure dominated strategy, i.e. a strategy the he should never use no
matter what strategy the row plater use?
(c)(2 pts.)Find one Nash equilibrium in the game.
(e)(2 pts.)Could you find another Nash equilibrium, pure or mixed, in this
game?
5.Monopolist X provides a product with no cost and he has 10 retailers to sell
the product. If retailers set different price, consumers will first visit the
retailer who offers the best service and then purchase from the shop with the
lowest price. For every retailer, if she provides more service to an
inquiring customer, she bears a higher service cost c. On the other hand, the
value of the product to the customer will increase by v, where v=3ln(c+1). X
has to decide how to set the wholesale price p0 and how to set the minimum
retail price p1 (p1>p0) for his retailer to maximize his own profit.
(a)(2 pts.)Given p0 and p1, how much will a retailer spend to serve one
customer?
(b)(3 pts.)Given p0, what's the optimal p1? (Give the answer in terms of p0.)
(c)(2 pts.)What is the optimal p0?
(按:老師於考試時應要求假設市場需求函數為q=100-p)
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