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課程名稱︰個體經濟學
課程性質︰必修
課程教師︰黃貞穎
開課學院：社科
開課系所︰經濟系
考試日期（年月日）︰2012/4/16
考試時限（分鐘）：180min
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
1.Consider a monopolist firm that produce output according to the following
production function:
0.5 0.5
Q=K L
where Q stands for output, K for capital, and L for labor. The demand for
the firm's output is given by Q=300-10P, where P is the price of the output.
The monopolist is a price taker in the input market.
Initially, the wage rate is $10 per labor-hour and the rental rate on capital
is $2.5 per machine-hour. At these input price, the firm optimizes by using
50 labor-hours and 200 machine-hours to produce 100 units of output that are
sold at a price of $20 (Take my word for it. Don't recalculate unless you
want to kill time!)
Suppose the wage rate rises to $22.5 per labor hour.
(a)(8%)If the firm were to continue to keep producing 100 units of output,
how much labor and capital would it use in this hypothetical situation?
(b)(8%)The firm could adjust its output level. Find the firm's new profit
mazimizing output level, mix of inputs, price, and the amount of profit
it earns in the long run.
(c)(10%)Supposr we apply what we have learned in consumer theory to this
question.Let us define the "factor subsitution effect" as the change in the
firm's optimal input mix when relative input price change, holding the
level of output constant. Similarly, define the "output effect" to be the
change in the firm's use of inputs when it adjusts tha amount of output
it produces, holding relative input prices fixed. Define an input to be
normal if its output effect is positive, that is, when the output level
increases, its use due to output effect increases as well.Likewise, define
an input to be inferior if its output effect is negative, that is,
when the output level increases, its use due to output effect decreases.
Calculate the factor substitution effect and the output effect.
In such input normal or inferior? Illustrate your calculation by an
isoquant-isocost diagram.
(d)(10%)Suppose we define an input to be Giffen if when its price increases,
the use of it increases by the monopolist.
Is it possible to have a Giffen input? Explan.
2.Eva Airlines has two potential customers: Jane and Elizabeth. Both demands
are in discrete amount. Jane is willing to pay up to 10 dollars for the
first trip, 10 more dollars for the second trip, 5 more dollars for the
third trip. 5 more dollars for fourth trip, 5 more dollars for the fifth trip.
For the sixth trip and onward, she is not willing to pay anything more.
Elizabeth is willing to pay up to 10 dollars for the first trip and 6 dollars
for the second trip. For the third trip and onward, she is not willing to
pay anthing more. Eva Arlines has zero fixed cost and zero marginal cost.
(a)(8%)If Eva Airlines cannot perform any form of price discrimination (so
it only sets a single price), derive the optimal price that maximizes
Eva’s profit. How much profit does Eva Airlines earn?
(b)(8%)If Eva Airlines can perform the first-degree price discrimination, how
many outputs will it sell to Jane and Elizabeth respectively? How
much in total will it charge Jane and Elizabeth respectively?
(c)(8%)Suppose Eva Airlines performs the second-degree price discrimination,
so it screens customers by providing two packages. Each package
consists of a quantity and a take-it-or-leave-it charge. For instance, if
a package (x,T) is offered, then a customer can pay the total amount
T to get a quantity of x of air travel service. Since Eva Airlines cannot
tell apart its two customers, it decides to offer one package (xj , Tj )
aimed for Jane and another package (xe,Te) aimed for Elizabeth.
Jane and Elizabeth supposedly will self select.Use the theory you have
learned from the second-degree price discrimination to derive the optimal
amount Te, Tj, xe, xj.
(d)(8%)Suppose Eva performs third-degree price discrimination. It can tell
apart Jane and Elizabeth. How much will it charge Jane per trip? How much
will it charge Elizabeth per trip? How much does it earn in total?
3.Consider an industry with 4 firms, each having marginal cost and fixed
cost equal to 0. The inverse demand curve facing this industry is
P(Q)=60-Q
where Q = q1 + q2 + q3 + q4 is total output.
(a)(8%) If each firm behaves as a Cournot competitor,what is firm 1's best
response function or reaction function — that is, firm 1's optimal
choice given other firms' outputs?
(b)(8%) Calculate the Cournot equilibrium.
(c)(8%)Firms 2 and 3 decided to merge and form a single firm with marginal
cost and fixed cost still equal to 0. Calculate new industry Cournot
equilibrium. Is firm 1 worse off or better off as a result? Was it a
good idea for firms 2 and 3 to merge?
(d)(8%)Suppose firm 1 can commit to a certain level of output in advance. If
the choice of firm 1 is q1, what would be the optimal choices of firms
2, 3 and 4? (Hint: After observing q1, firms 2, 3 and 4 would engage in
(Cournot) three-firm competition.) What is the optimal level of q1?
Calculate profits of firm 1 and compare it with (b). Is firm 1 better
off or worse off?
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