国际经济学国外教授出的考试题

CSUF

2011 Fall

Econ531

Homework 01

Instructions: Please answer Question #6 and any four questions from Question 1 through Question 5. Please submit your answer (attach your file electronically) before 11:59 PM, Monday, September 26. Please show your work in all cases. Good Luck!

1.This question is about producer surplus and consumer surplus.

a.Given a linear demand curve, if domestic consumption changes by

10%, does consumer surplus also change by 10%? Why or why not?

What is the relationship between change in domestic consumption and

consumer surplus?

b.Is there a difference between producer surplus and profit? Explain.

2.Suppose Robinson Crusoe produces fish (F) and coconuts (C). Assume that

during a certain period, he has decided to work 200 hours and is indifferent to whether he spends this time fishing or gathering coconuts. Robinson

Crusoe’s production function for fish is given by:

And his production function for coconuts is given by:

where L F and L C are the number of hours spent fishing or gathering coconuts. Consequently:

200

Robinson Crusoe’s utility for fish and coconuts is given by: √ .

(a) Write an equation for Crusoe’s PPC.

(b) Show that (explain in words) if Robinson Crusoe cannot trade with rest of the

world, he will choose to allocate his labor such that slope of his PPC will equal the slope of his indifference curve (i.e., his marginal rate of product transformation (MRT) will equal his marginal rate of substitution (MRS) on the consumption side.).

(c) Specifically, for this case, show that his:

(d) What will the optimal values of his F and C be?

(e) Suppose now that trade opens up to Robinson Crusoe and he can now trade fish and coconuts at a price of one fish for two coconuts. If Robinson Crusoe continues to produce the same quantities of F and C as before, what will he choose to consume once he is given the opportunity to trade?

3.Assume that good X is a labor-intensive good and good Y is a capital-

intensive good; country A is labor-abundant and country B is capital-

abundant. But suppose that as w/r rises, after a point, good X in fact

becomes more capital-intensive than good Y.

a.Is this "factor intensity reversal" plausible? Explain.

b.Show this phenomenon on the Fountain Diagram.

c.Show this phenomenon on the Edgeworth Box diagram.

d.Show this phenomenon on the Iso-quants drawn over K and L.

4.The following equations describe the long-run situation for prices and costs,

where the numbers indicate the amounts of labor and land needed to produce

a unit of corn and toys.

P corn = 80W + 40R

P toys = 100W + 30R

a.If the price of corn is initially 200 and the price of toys is initially 200,

what are the values for the wage rate W and the rental rate R?

b.The price of corn now increases to 240. The price of toys stays the