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Question 1 Let an individual's utility function be given as u(x1, x2) = 2 x1 x2 . a) Compute the Marginal Rate of Substitution. b) Initially, the individual consumes bundle (x1 = 100, x2 = 12.5). Then, the individual's consumption of the first good is cut to x 0 1 = 50. What is the new level of consumption of good 2, x 0 2 , that the individual needs to consume in order to reach the same utility level as before? c) Given the prices p1 = 1 and p2 = 2 for the first and the second good, respectively, and a budget of m = 100, what is the best consumer choice? d) Find the individual's general demand function for good 2. e) If the price for the first good rises to p 0 1 = 50, how much less of good 2 will the individual conusme? f) Assuming the demand function for good 1 is x1(p1) = 1 2 m p1 , what is the inverse demand funtion, and what is the own-price elasticity of demand for good 1! g) Assuming the demand function for good 1 is x1(p1) = 1 2 m p1 , show mathematically that the good is not inferior.

Question 2 An individual's preferences over consumption bundles A, B, and C are given as A B B C A C Are these preferences transitive? Explain why or why not!

Question 3 The demand function is given by x = A p with x giving the demand, p the price and a and as positive parameters. a) Derive the price elasticity of demand, . What is the economic meaning of the price elasticity of demand? What is elastic, what is inelastic demand? b) Denote revenues as a function of demand x and price p. How do revenues change as a reaction to an increase of the price, if demand is inelastic? c) Is the good in focus a Giffen good? Explain your answer both verbally and analytically.

There are two consumers who consume good x (private good) and good y (public good).

The sum of consumption between both consumers = T (T1+T2)

price of a private good x= $1

Price of a unit T = $2

Income = $100

Utility function:

U = log X + log(T1 + T2 )

Use the given utility function along with prices, and income to find...

a. socially optimal (efficient) level of production of a public good.

b. market (private) level of provision of a public good

There are two consumers who consume good x (private good) and good y (public good).

The sum of consumption between both consumers = T (T1+T2)

price of a private good x= $1

Price of a unit T = $2

Income = $100

Utility function:

U = log X + log(T1 + T2 )

Use the given utility function along with prices, and income to find...

a. socially optimal (efficient) level of production of a public good.

b. market (private) level of provision of a public good.

[9:04 PM, 12/8/2021] Fridah: There are two consumers who consume good x (private good) and good y (public good).

The sum of consumption between both consumers = T (T1+T2)

price of a private good x= $1

Price of a unit T = $2

Income = $100

Utility function:

U = log X + log(T1 + T2 )

Use the given utility function along with prices, and income to find...

a. socially optimal (efficient) level of production of a public good.

b. market (private) level of provision of a public good. [9:23 PM, 12/8/2021] Fridah: There are two consumers who consume good x (private good) and good y (public good).

The sum of consumption between both consumers = T (T1+T2)

price of a private good x= $1

Price of a unit T = $2

Income = $100

Utility function:

U = log X + log(T1 + T2 )

Use the given utility function along with prices, and income to find...

a. socially optimal (efficient) level of production of a public good.

b. market (private) level of provision of a public good.

1. (25 points) Suppose two countries: Zimbabwe and Zambia, use only capital (K) and labor (L) for production. Zimbabwe has 2,075 units of capital and 932 units of labor, and Zambia has 832 units of capital and 295 units of labor. Both countries produce two goods: Cloth and Phone. In Zambia, there are 384 units of capital and 176 units of labor employed in the phone industry. In Zimbabwe, there are 956 units of capital and 632 units of labor employed in the phone industry. a. (4 points) Which country is labor abundant? Which country is capital abundant? Which good is labor intensive? Which good is capital intensive? b. (4 points) Assume identical preferences and technologies between the two countries. Use graphical analysis to present the autarky equilibrium in each country. Which country will have lower relative price of phone in autarky? c. (4 points) Use graphical analysis of the relative demand and relative price of labor in terms of capital for each industry to show how the equilibrium relative price of labor and the equilibrium relative quantities of labor in each industry are determined in Zambia. d. (4 points) Suppose now that the countries open to trade. What will happen to the relative price of phone in Zambia? Show the new trade equilibrium in Zambia on your graph. Clearly indicate how much phone will be produced and consumed in Zambia after the country opens up to trade. What is the good that Zambia will export? e. (4 points) Use graphical analysis to show the effects of trade on the relative factor prices and relative factor demands in Zambia. Put relative wage on the Y-axis and relative labor on the X-axis. Write a clear statement about the direction of the relative factor price change and the changes in relative labor demand in each sector. What will happen to real wages and real rental on capital in Zambia? f. (5 points) (Standalone question): (True/False) According to the standard Heckscher-Ohlin model with two factors (capital and labor) and two goods, the movement of Turkish migrants to Germany would decrease the amount of capital-intensive products produced in Germany. Explain.