推 TINTINH :已收精華區:) 02/08 04:05
課程名稱︰區域經濟學一
課程性質︰必修
課程教師︰彭信坤
開課學院：社會科學院
開課系所︰經濟系
考試日期（年月日）︰2009.11.23
考試時限（分鐘）：180min
是否需發放獎勵金： 是
（如未明確表示，則不予發放）
試題 :
Regional Economics - I
Midterm Examination
14:20 - 17:20, Nov 23, 2009
323 M2450
Institute of Economics, National Taiwan University
1. Consider a linear spatial market, the demand function for the consumer in
each location x is given by q(x)= a - [p(x)+tx], where a denotes the
reservation price of consuming the good for the consumer in the each location
x, in which the monopoly is produced in the location 0, thus the location x
represents the distance between firm's location and consumer's location, and
the t is the transportation cost of good per unit distance, thus the p(x) is
the full price which the consumer locate at x should pay, if the firm can
choose both the market size R and the price of the product, then, please find
(40%)
(i), the optimal price and the market size under the mill pricing, PU*, RM*.
(ii), if the spatial monopoly adopt the discriminatory pricing for the
consumer in the different location, then please find
(a), the optimal discriminatory pricing PD*(x),
(b), the demand elasticity in each location x, εD*(x)
(c), the relationship between the demand elasticity εD*(x) and location
x,
(d), the optimal market boundary RD*.
(iii), Based on the previous analysis, which pricing policy is more prefer for
the firm under the variable market size?
2. In the market of "alcohol", the consumer preference for the "degree of
liquor" on the alcohol is during 8%-48%, and the consumers preference with
liquor degree during 8% and 48% is uniform distribution, and assume that
every consumer buys only one unit of this alcohol, and its utility of the
consumer associated with the preference q with purchased the liquor from
firm i is specified by U(x) = a - p(xi) - c(q-qi)^2, where a denotes the
reservation price of consuming the alcohol for the consumer associated
with the preference q, in which the reservation price is identical for all
the consumers with the preference over q in [8%,48%], the marginal cost
of producing the alcohol by each firm is identical and given by k, then(40%)
(i), if the production on the degree of the alcohol for both firms is
constrained with qi in [8%, 48%], and both firms compete the choice of the
degree of alcohol (First stage), then price determination(Second stage),
please find the equilibrium prices, the degree of the alcohol, and the
profits with Nash game for both firms;
(ii), if there is not any constrain for the degree of the alcohol to be
produced by the both firms, that is, the firm can produce the alcohol with
any degree, then follow the previous two-stage game, both firms can
determine both the degree of the alcohol as well as prices to maximize
their profits, then please find the Nash equilibrium degree of the alcohol
, price, and profit for both firms.
(iii), how to interpret the equilibrium result between assumption with
constrain and non-constrain?
3, In the Linear (horizontal) spatial competition model, what kinds of
variables can be employed as a decision variable by the firm, and what kinds
of game has usually played by the firms in the literature? And what kinds of
the results would be derived? Is any constrain for the model specification?
Please make a comparison for these results with various competition schemes,
and try to interpret its economic intuition under different competition
scheme. Please interpret the equilibrium of the vertical product
differentiation in the Bertrand competition(20%)
* About question 2, it is assumed that the negative degree is not meaningless.
--
Nobody ever saw a dog make a fair and deliberate
exchange of one bone for another with another dog.
--
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