課程名稱︰資訊經濟
課程性質︰資管系選修
課程教師︰孔令傑
開課學院：管理學月
開課系所︰資管系
考試日期（年月日）︰110.04.19
考試時限（分鐘）：180
試題 :
1. (30 points) A manufacturer sells a product to a newsvendor retailer. The un-
it production cost is c > 0 dollars, where 0 < t < 1, the unit retail price is
p > 0 dollars, the wholesale price is w ≧ 0, and the random demand faced by t-
he retailer is uniformly distributed between 0 and 1. If the sales quantity re-
aches t ≧ 0 untis, tge nanufacturer pays the retailer b ≧ 0 dollars as a bon-
us. Note that the bonus is paid at most once and thus not for each unit sold.
The retailer choose an order quantity q units to maximize its own expected pro-
fit. ALl quantities except q are exogenous.
(a) (5 points) Suppose that the two players are integrated. Find a production
quantity q^{FB} that mazximizes the channel profit.
(b) (10 points) Suppose that he two players are not integrated. Formulate the
retailer's profit maximization problem.
(c) (10 points) Find an order quantity q^* that is optimal for the retailer.
(d) (5 points) Is it possible for the players to find a set of values for t, b
, and w to coordinate the channel? Argue with mathematical derivations and eco-
nomic intuitions.
2. (30 points; 10 points each) Two restaurants (for each of them, she) compete
in delivering meals to consumers (for each of them, he). If a type-θ consumer
orders from restaurant i, i in {1,2}, his utility is v - p_i - θt_i, where v
. 0 is the utility if enjoying the meal, p_i is the meal price (including the
delivery fee), and t_i is the delivery time. Consumers are different onlu in t-
heir sensitivity of waiting, i.e., θ. It is assumed that θ is uniformly dist-
ributed within 0 and 1, t_1 and t_2 are exogenous, and 0 < t_1 < t_2. THe two
restaurants determine their prices simultaneously. Each of them acts to mzximi-
ze her own profit, where the unit cost of making a meal is c for both of them.
All consumers then simultaneously choose to order from restaurant 1, order from
restaurant 2, or order nothing. Each of them acts to maximize his utility.
(a) Given p_1 and p_2, derive the demand volume for each of the two restaurants
(b) Formulate the two restaurants' profit maximization problems.
(c) Find the two restaurants' equilibrium prices.
3. (30 points; 10 points each) A firm (she) produces and sells two types of pr-
oducts to two types of consumers (for each of them, he). The product quality a-
nd price of product i are q_i and p_i, i = 1,2, respectively. If a type-θ con-
sumer purchases product i, his utility is θq_i - p_i. THe probability for a c-
onsumer to be of type θ_1 and θ_2 are β and 1 - β, where 0 < θ_1 < θ_2.
The unit production cost of product i is cq_i^2/2, i = 1,2. The firm cannot ob-
serve a consumer's type. She plans to choose the quality levels and prices for
the two products to maximize her expected profit while inducing the type-θ_i
consumer to buy product i, i=1,2.
(a) Formulate the firm's profit maximization problem.
(b) Solve the firm's problem to find the optimal quality levels.
(c) Suppose that the firm can observe a consumer's type. Formluate and solve t-
he firm's profit maximization problem when facing either type of consumer. Then
comment on your answer in Part (b) regarding efficiency and distortion. Argue
with mathematical derivations and economic intuitions.
4. (30 points; 15 points each) A nightclub is setting prices p_B and p_G for b-
oys and girls., respectively. By going to the nightclub, a type-θ boy's utili-
ty is θ + α_Bn_G - p_B, where θ is his willingness to pay when there is no
girl, α_B is the degree of cross-side network externality from girls to boys,
i.e., and n_G is the number of girls in the nightclub in equilibrium. Note that
the boy is willing to pay more to the nightclub if there are more girls there.
Similarly, a type-η girl's utility is η + α_Gn_B - p_G, where α_G is the d-
egree of cross-side network externality from boys to girls. Both θ and η are
uniformly distributed within 0 and 1. It is assumed that α_B > α_G > 0, i.e.,
each additional girl gives a boy a higher utility than that each additional boy
may give to a girl. One goes to the nightclub if and only if her/his utility is
nonnegatice. After the nightclub announces p_B and p_G, all boys and girls dec-
ide whether to go to the nightclub simultaneously. Each of them act to maximiz-
es her/his utility.
(a) Given p_B and p_G, find the equilibrium numbers of boys and girls going to
the nightclub. Then formulate the nightclub's profit maximization problem by a-
ssuming that there is no service cost. Do not attempt to solve it.
(b) Suppose that the nightclub plans to charge only one side of consumers. If
it fixes p_B = 0 and optimizes p_G only, what is an optimal price? What if it
is p_G that is fixed to 0? Determine which side should be the nightclub's reve-
nue source if pnly one side may be charge. Argue with mathematical derivations
and economic intuitions.