課程名稱︰個體經濟學一
課程性質︰必修
課程教師︰古慧雯
開課學院：社會科學院
開課系所︰經濟系
考試日期（年月日）︰102/11/11
考試時限（分鐘）：110分鐘
試題 :
個體經濟學期中考 (2013.11) 古慧雯
總分30分。答題皆須附說明，未做解釋的答案概不計分。
1. A consumes two goods and his utility function is:
u = xy.
Let I, p_x and p_y denote the income, price of c and price of y. It is
obvious that A's optimal consumption bundle is always an interior solution.
(a) (1 point) Please calculate the marginal value of in terms of y (|dy/dx|).
(b) (1 point) Does A have a convex preference?
(c) (2 points) Please solve for A's optimal consumption bundle in
terms of I, p_x and p_y.
(d) (2 points) Please calculate A's price elasticity of demand for x.
(e) Suppose that originally I = $60, p_x = $2 and p_y = $1. Now p_x
decreases to $1.
i. (2 points) Please calculate the substitution effect and income
effect (Δx, Δy). Feel free to express your answer in terms of √2.
ii. (2 points) Please calculate the Laspeyres price index L in this case.
2. (2 points) Suppose that the amount of time required for the electrician or
the carpenter to complete a job of rewiring or paneling is given by the
following table.
rewiring (hours) paneling (hours)
─────────────────────────
electrician 5 10
carpenter 10 15
Who has the comparative advantage at rewiring, and why?
3. Consider the production function:
1/4
x = (lk) ,
where x denote the output, and l and k are two factors.
(a) Consider first the long-run problem.
i. (2 points) What do you expect the shape of the long-run average cost
function to be? Do you expect it to be an increasing or a decreasing
function, and why?
ii. (1 point) For any x > 0, do you expect the marginal cost or the
average cost to be larger, and why?
iii. (1 point) Please calculate the marginal rate of technical
substitution (|dk/dl|).
iv. (2 points) The price of factor l is $1, and the price of factor k
is $16. Please derive the expansion path. (Express k as a function
of l).
v. (2 points) Please derive the long-run total cost function.
(b) (2 points) Suppose k is fixed to be 1 unit in the short run. At what
output level do you expect the short-run total cost and the long-run
total cost are equal, and why?
4. A comic book company pays an annual licensing fee of $10,000 for the rights
to an artist's character. Please explain how the readers become affected
when the following events take place. (We assume that the marginal revenue
of comic books decreases with sales and the marginal cost is an increasing
function.)
(a) (2 points) An increase in price of paper.
(b) (2 points) An increase in the artist's licensing fee.
5. Dizzyland Amusement Park has begun selling a VIP pass that costs$20 and
entitles the bearer to a discount price on rides. Mickey Duck, as Dizzyland
patron, has decided he is definitely happier buying a VIP pass than not
buying one.
(a) (2 points) In a diagram with "Rides" on the horizontal axis and "All
Other Goods" on the vertical axis, illustrate the shift in Mickey's
budget line when he buys the pass.
(b) (2 points) Consider that Mickey Duck has a convex preference, and his
optimal consumption bundle is an interior solution. In your previous
graph, please show where his old consumption bundle could be when no VIP
pass was offered, and explain clearly. Furthermore, is it true that
Mickey will certainly go on more rides now that he has a VIP pass?
Exam201311.ctx