Homework 1-

1. Review of math:

a. You are told that there are two linear relationships between Y and X where Y is the variable measured on the vertical axis and X is the variable measured on the horizontal axis. The first linear relationship is given by the equation Y = 50 - 2X. You are told that the second linear relationship goes through the origin and that for every 1 unit increase in the X variable, the Y variable increases by 8 units. What is the equation for the second line and what is the solution (X, Y) for your two equations?

b. You are told that there are two linear relationships between Y and X where Y is the variable measured on the vertical axis and X is the variable measured on the horizontal axis. The first linear relationship contains the points (125, 75) and (50, 150). The second linear relationship contains the points (50, 100) and (150, 150). Find the equations for the two lines and then calculate the solution (X, Y) for these two equations.

c. Hint: this one is  a bit more challenging!) You are told that there are two linear relationships between Y and X where Y is the variable measured on the vertical axis and X is the variable measured on the horizontal axis. The first linear relationship is described as follows: the Y variable is equal to 5 more than twice the X variable. The second linear relationship is described as follows: the X variable is equal to 5 less than twice the Y variable. Find the equations for the two lines and then calculate the solution (X, Y) for these two equations.

2. More math review:

a. You have three hundred books and you decide to purchase an additional one hundred books. What is the percentage increase in books?

b. You have four hundred books and you decide to decrease your personal library by selling one hundred books. What is the percentage reduction in books?

c. Look at your answers in parts (a) and (b). Are your answers the same in absolute value terms or are they different? Explain this similarity or this difference. 

3. Absolute and Comparative Advantage:

Suppose Joe and Mary both have 1 hour available to spend in some combination of cleaning baths and washing dishes. You are told that Joe can clean one bath in 10 minutes or wash one set of dishes in 20 minutes. Mary can clean one bath in 5 minutes or wash one set of dishes in 15 minutes.

a. Draw two graphs representing Joe's PPF and Mary's PPF. In your graph measure clean baths on the horizontal axis. Label your graphs carefully and completely. Assume in drawing the two PPFs that they are linear.

b. Fill in the blank:

__________ has the absolute advantage in cleaning baths.

___________ has the absolute advantage in washing dishes.

___________ has the comparative advantage in cleaning baths.

___________ has the comparative advantage in washing dishes.

c. Joe's apartment has three dirty baths and 2 sets of dirty dishes while Mary's apartment has 6 dirty baths and 2 sets of dirty dishes. Assume that Joe and Mary both have 1 hour they can devote to washing dishes and cleaning baths. If they do not specialize and trade, is it possible for Joe to get his apartment clean in the allotted time? Explain your answer.

d. Joe's apartment has three dirty baths and 2 sets of dirty dishes while Mary's apartment has 6 dirty baths and 2 sets of dirty dishes. Assume that Joe and Mary both have 1 hour they can devote to washing dishes and cleaning baths. If they do not specialize and trade, is it possible for Mary to get her apartment clean in the allotted time? Explain your answer.

e. Suppose that Joe and Mary decide to specialize and trade. Will this make it possible for both Joe and Mary to successfully clean the dirty baths and wash the dirty sets of dishes? Explain your answer.

f. What is the range of prices in terms of washed sets of dishes that 1 clean bath will trade for in this example?

4. Review of Supply and Demand:

Suppose there is a small closed economy where the market for gadgets can be described as follows:

Domestic Demand for Gadgets: P = 1000 - Qdom

Domestic Supply of Gadgets: P = 200 + Qdom

Where P refers to the price per gadget and Qdom refers to the domestic quantity (this could be the domestic quantity demanded or the domestic quantity supplied). Assume the market for gadgets in this small economy is currently closed to trade with other countries.

a. Find the equilibrium price and quantity of gadgets in this small closed economy. In addition, find the value of consumer surplus, producer surplus, and total surplus.

b. Suppose the world price of gadgets is $800. If this small economy opens to trade, what will happen? In your answer provide a numerically specific answer with regard to the level of exports or imports, the quantity of gadgets domestically supplied, the quantity of gadgets domestically demanded, the value of consumer surplus with trade, the value of producer surplus with trade, and the value of total surplus with trade.

c. Who benefits in the domestic economy when this small closed economy opens to trade and the world price of gadgets is $800?

d. Suppose the world price of gadgets is $400. If this small economy opens to trade, what will happen? In your answer provide a numerically specific answer with regard to the level of exports or imports, the quantity of gadgets domestically supplied, the quantity of gadgets domestically demanded, the value of consumer surplus with trade, the value of producer surplus with trade, and the value of total surplus with trade.

e. Who benefits in the domestic economy when this small closed economy opens to trade and the world price of gadgets is $400?

5. Review of Supply and Demand: Tariffs and Quotas (continuation of problem 4):

The small closed economy described in problem (4) is our starting point for this problem. The economy has the given domestic demand and domestic supply curves. And, you know that the world price for a gadget is $400.

a. Suppose that this economy is open to trade, but that the legislature has passed a tariff on imported gadgets so that the price of gadgets in this economy with the tariff is now $500. How many gadgets will be imported into the small economy given this information?

b. Using the above information and assuming the imposition of the tariff described in part (a),  calculate the consumer surplus with the tariff, the producer surplus with the tariff, the tariff revenue received by the government, and the deadweight loss due to the tariff.

c. Using the above information and assuming the imposition of the tariff described in part (a), compare the value of consumer surplus, producer surplus, and total surplus for this economy when this market is closed to trade, open to trade, and when the tariff is imposed. Summarize your findings in a table that illustrates these three possible trade situations and clearly presents the data needed to compare these situations. (Hint: imagine that you are presenting to your CEO and are trying to make sure he gets a quick sense of how these three situations compare to one another-her time is valuable and you want to make a strong, clear, short presentation because you know your next promotion depends on how you handle this situation!)

6. Review of Supply and Demand: Tariffs and Quotas (continuation of problem 4)

The small closed economy described in problem (4) is our starting point for this problem. The economy has the given domestic demand and domestic supply curves. And, you know that the world price for a gadget is $400.

a. Suppose that this economy is open to trade, but that the legislature has enacted a quota on imported gadgets so that the price of gadgets in this economy with the quota is now $500. How many gadgets will be imported into the small economy given this information?

b. Using the above information and assuming the imposition of the quota described in part (a),  calculate the consumer surplus with the quota, the producer surplus with the quota, the license holder revenue received by the importer, and the deadweight loss due to the quota.

c. Using the above information and assuming the imposition of the quota described in part (a), compare the value of consumer surplus, producer surplus, and total surplus for this economy when this market is closed to trade, open to trade, and when the quota is imposed. Summarize your findings in a table that illustrates these three possible trade situations and clearly presents the data needed to compare these situations. (Hint: imagine that you are presenting to your CEO and are trying to make sure he gets a quick sense of how these three situations compare to one another-her time is valuable and you want to make a strong, clear, short presentation because you know your next promotion depends on how you handle this situation!)

7. Compare your results in problem (5) and problem (6). Do your results suggest that there is any great difference in outcome with the imposition of the described tariff versus the described quota? Explain your answer fully.