课程名称︰个体经济学
课程性质︰经济系必修
课程教师︰古慧雯
开课学院：社会科学院
开课系所︰经济学系
考试日期（年月日）︰2014/11/10
考试时限（分钟）：120 mins
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
(满分 26 分)
1. The production function of a manufacturer is as follow:
q = √(lk)
where q denotes the output, l denotes units of labor and k denotes units of capital.
The price to hire a unit of labor is $1, and the price to hire a unit of capital is $9.
(a) We first consider the production in the long run when the quantity of either factor
can be freely adjusted.
i. (1 pt) Does the production exhibit increasing returns to scale, constant
returns to scale, or decreasing returns to scale?
ii. (2 pts) Please calculate the marginal rate of technical subsitution of labor
for capital, MRTS≡|dk/dl|.
iii. (2 pts) Please place l on the horizontal axis and k on the vertical axis, and
draw the expansion path.
iv. (2 pts) Please derive the long-run total cost function LRTC(q).
(b) In the short run, k is fixed to be 4 units while l can be freely adjusted.
i. (2 pts) Please derive the short-run total cost function SRTC(q).
ii. (2 pts) At which quantity will the short-run average cost and the long-run
average cost be the same?
2. A consumes only two commodities: x and y. His utility function is:
u(x,y) = xy^2
Currently, the price of x, p_x, is $1, the price of y, p_y, is $2, and A's income, I, is $12.
(a) (2 pts) Please derive A's Engel curve for x.
(b) (1 pt) Please calculate the income elasticity for good x.
(c) (2 pts) Please calculate the cross elasticity for x with respect to y.
(d) (3 pts) Suppose p_y increases from $2 to $4, while p_x and I remain the same. Please
calculate the substitution effect and the income effect due to this change.
3. Marijuana consumption was considered legal in country X before. The market was competitive,
and every participant was a prcie-taker. The monthly market demand was:
Q_d = 130-p,
where Q_d is the quantity demanded. There is no production of marijuana in country X, and
the drug dealer need to purchase it abroad. The amount they purchased each month depended
on the price of marijuana in country X, p:
Q_m = p,
where Q_m is the quantity of marijuana obtained from abroad.
(a) (1 pt) Find the equilibrium price of marijuana in country X.
(b) Marijuana consumption is now announced illegal in country X, and customs officers will
search arriving travelers for the drug. The chance that smuggled marijuana at customs
will be found and confiscated is 1/3.
i. (1 pt) How does the new policy affect market demand for marijuana in country X?
ii. (1 pt) How does the new policy affect the relationship between Q_m and p?
iii. (2 pts) Find the equilibrium price of marijuana in country X after the policy change.
4. (2 pts) In Japanese colonial Taiwan, a tenant paid a fixed amount of his crops, say 500 picul
paddy, to his landlord each year. The Nationalist Government found that on average, a tenant
gave half of his harvest to the landlord. (It was more (less) than one half when the harvest was
poor (good).) 陈诚 considered the arrangement unfair to tenants and announced “三七五减租” in
1949. The government first found out the harvest of a tenant in an average year, say 1,000 picul
paddy, and then stipulated that the landlord could collect only 375 pical paddy (instead of 500
pical paddy) from this tenant. Please discuss how “三七五减租条例” affected a tenant's
incentive to work and his harvest.