課程名稱︰個體經濟學上
課程性質︰必修
課程教師︰蔡崇聖
開課學院：社會科學院
開課系所︰經濟學系
考試日期（年月日）︰2022/01/10
考試時限（分鐘）：
試題 :
1. [35%] There are many homogeneous firms operating in a perfectly competitive
market of a constant-cost industry. Every firm uses the following production
function with inputs labor (L), capital (K) and Materials (M):
f(L,M,K) = √(L(K+M))
Suppose that wage is w = 4, the interest rate is r = 1, and the price of
material is m = 7.
a. [3%] What kind of returns to scale does this production function exhibit?
b. [6%] Suppose that K = M = 2 in the short run. Find the short-run total
cost (STC), average cost (SAC), average variable cost (SAVC), and marginal
cost (SMC) functions.
c. [5%] Suppose that in the long run, both K and M can be adjusted. Write
down the cost minimization problem. Find the optimal amounts of factors,
L*, K* and M*, as functions of q. (Hint: K and M are perfect substitutes
in the long run.)
d. [4%] Following c., derive the long-run total cost (LTC) , the average
cost (LAC), and marginal cost (LMC) functions.
e. [6%] Based on what you found in b. and d., draw a figure to show the
relationship between SAC, SMC, LAC and LMC. Explain their relationship.
Is there any output level that makes SAC = LAC? If yes, what is it? If
no, explain why not.
In the following questions f. and g., use the following market demand
function:
Q(P) = 120 - 5P
f. [6%] Suppose that there are 20 firms operating in market in the short
run. What are the market equilibrium price and total output? How much
profit does each firm earn?
g. [5%] Find the long-run market equilibrium price and total output. Compare
them with those in the short-run equilibrium. Explain your finding.
2. [30%] The market for rubber tires is perfectly competitive. Each firm in the
market uses the following short-run total cost function (STC):
STC(q) = 18 + 2q + 2q^2.
There are currently 40 homogeneous firms in this market. The market demand is:
Q(P) = 18 - 10P.
a. [7%] Find the SAC, SAVC and SMC functions. Show that the SMC curve passes
through the minimum points of the SAC and SAVC curves. Draw a figure to
show them.
b. [3%] Find each individual firm's short-run supply function.
c. [8%] Compute the market equilibrium price and total output. How much profit
does each firm earn? Will firms stay in the market or shutdown in the
short run? Explain your answer.
d. [6%] Suppose that government imposes a commodity tax of $t on each unit of
rubber tires. Thus, the after-tax total cost function for each firm is:
STCt(q) = 18 + 2q +2q^2 + tq
It is decided that t = 2. Other things remain the same. Then what will be
the equilibrium total out put after the tax? What are the price that
consumers pay and the price that producers receive?
e. [6%] From the market's point of view, does this tax make the consumer,
the firm, and the society, respectively, better off or worse off? Explain
your finding. (Note: you need to precisely compute the changes in the
consumer surplus, producer surplus, and social welfare to answer the
question.)
3. [20%] "Taiwan's trade chief says no timetable for talks with Japan on
Fukushima food ban" by Matthew Strong 【Taiwan News, 2021.12.21】
"In a victory for the govvernment, a referendum proposal to ban the import
of pork products containing residues of the leanness drug ractophamin failed
to win a majority in the nationwide vote. Attention is now expeceted to
shift to a ban placed on food and agricultural products from the preferences
of Fukushima, Chibak, Gunma, Ibaraki, and Tochigi in the wake of the march
2011 Fukushima nuclear disaster. Minister without Portfolio John Deng, who
heads the Cabinet's Office of Trade Negotiations, said the country still
needs to face the issue, but it should be decided on the basis of health,
science, and international rules. He emphasized that there is not yet a
timetable for talks with Japan on the subject. The referendum result will
enhance Taiwan's chances of joining the Comprehensive and Progressive
Agreement for Trans-Pacific Partnership (CPTPP) trade group."
Now consider two markets in Taiwan: the market for Japanese agricultural
products and the market for domestic agricultural products. Both markets are
assumed to be perfectly competitive. Donestic products and Japanese products
are considered substitutes. There is currently a quota Q1 imposed on the
market of Japanese products. The equilibrium output without the quota is
supposed to be (P*1,Q*1). Apparently, Q1 < Q*1. On the other hand, the
current equilibrium (with the quota in the Japanese products market) in the
domestic products market is (P*2,Q*2).
a. [8%] If the quota in the Japanese products market is removed, other
things being the same, what will happen to the equilibrium in the Japanese
products market? By drawing a figure and a table for welfare analysis,
discuss how the removal will affect the consumer surplus and producer
surplus in this market. Who may be benefited/hurt from it? Explain your
answer.
b. [8%] Recall that domestic products and Japanese products are sibstitutes.
If the quota in the Japanese products market is removed, how will it
affect the equilibrium in the domestic products market? How will it
affect the consumer surplus and producer surplus in this market? Who may
be benefited/hurt from it? Explain your finding.
c. [4%] Consider a firm operating in the domestic products market. Suppose
that its cost structure does not change after the removal of the quota,
then what will happen to its output and shutdown decisions afterwards?
Draw a figure to explain your answer.
4. [15%] Determine whether each of the following statements is true or false.
a. [5%] If a firm has a technology that satisfies monotonicity, then its
marginal cost must be positive.
b. [5%] Suppose that every firm in a competitive market of a constant-cost
industry has a U-shaped LAC. Then when every firm's LAC decreases due
to some technological progress, there will be more firms staying in the
market in the long run.
c. [5%] Since SAC(q) >= LAC(q) at any q, the average product of labor in the
short run cannot be higher than that in the long run for a given q.