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1. Suppose that the economy produces three goods, raisins (R), soybeans (S), and textiles(T). What would its PPF look like under conditions of constant opportunity costs? What would it look like with increasing opportunity costs?

With three goods, the PPF is a three dimensional figure with three axes, R, S and T. With constant opportunity costs, the PPF is a plane. With increasing opportunity costs, the PPF is bowed-outward.  It resembles a sail, or "a bubble blown in a corner," as Allison Miles eloquently phrased it.

2. Using the following data, calculate the country's nominal and real GDP levels.

Use GDP = Ps S + Pt T to calculate nominal GDP. To calculate real GDP, divide nominal GDP by Pt, or use real GDP = S(Ps/Pt)+ T.

Case Ps S Pt T nominal GDP real GDP
a. $5 20 $1 15 $115 115T
b. $10 20 $2 15 $230 115T
c. $4 40 $8 12 $256 32T
d. $4 60 $8 18 $384 48T

3. Using your calculations from question 2, compare changes in nominal and real GDP between cases a and b. Explain your result.

Real GDP is the same in both cases because real output (units of S and units of T) is the same. Only the prices have changed. Since the prices doubled, nominal GDP doubled as well.

Note that cases C and D use the same prices, but that the quantities of both goods are 50% higher in case D than in case C. Thus real GDP is 50% higher as well.

4. Suppose the economy is characterized by constant opportunity costs so that Ps/Pt = 1.5 (yd. T/bu. S). Derive the economy's national supply schedule How does it differ from the one derived in figure 2.8?

National Supply

A relative price greater than 1.5 would produce a corner solution, with no T production and maximum output of S. A relative price below 1.5 would also result in a corner solution: no S would be produced; producers would maximize T output. Note that under conditions of constant opportunity costs, demand plays no role in determining relative prices in the model; these are determined only by supply. However, demand determines the quantity of each good produced. See the slides for the graph of NS under conditions of constant opportunity cost (slides #94, 101 & 103 for Fall '07).

5. Suppose that in world markets, the relative price of S is lower than A's autarky price. Once trade is allowed, would A be a net exporter or importer of S? What would be the case for good T in country A in this situation?

A's autarky prices reflect its opportunity costs. If the world's relative price of S is lower than A's autarky price, then A's residents may import S more cheaply than they could make or buy it at home. A's S industry will contract and eventually disappear.  The resources released will eventually all be absorbed by A's expanding T industry. Clearly A will be a net importer of S and a net exporter of T.

6. Refer to problem 4. Derive country A's national supply and demand curves for good T. Be careful how you label the axes!

Follow the example in text Figure 2.8 -- I will derive the NS and ND for S in the constant opportunity cost case in class.  When you derive the NS for T, be sure that the relative price of T (Pt/Ps) is on the y axis and the quantity of T is on the x axis.

7. If a country is at a point on its PPF where the slope of the PPF is flatter than the slope of the CIC touching that same point, then the standard of living would rise if outputs of the two goods would change so as to move down the PPF. True or false? Demonstrate and explain.

This statement is true. It describes a point such as H on the following graph. The slope of the PPF is the cost of producing one more unit of S. The slope of the CIC is the value to society of one more unit of S. At point H, society is willing to pay more than it would cost to produce one more unit of S. Hence, increasing S production will increase the standard of living.

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8. Suppose that country A produces two goods under conditions of constant opportunity costs. Given its resources, the maximum S that it can make is 500 units, and the opportunity cost of making T is 2. What is the maximum amount of T that it can produce? Draw a graph and explain.

Note that in the question the units must be expressed in S. That is, the opportunity cost of making 1T is 2S. Therefore the maximum amount of T that could be produced is computed as follows:PPF
500S (1T/2S) = 250T.

9. Suppose that a country produces two goods, X and Y, with two factors of production, K and L. The production of good X always requires more K per unit than does the production of good Y. What does this imply for the shape of the country's PPF? Explain carefully.

In this case, the PPF will be concave to the origin, that is, it will be bowed out. Why? Suppose that you start from a point of complete specialization in the production of Y. Think about the logistics of expanding the production of X. Initially, industry Y has all of the resources. If X is to expand, it must obtain resources from Y. Since Y utilizes less K per unit than does X, as it begins to contract, the Y sector will probably idle relatively more K than L.  But high ratios of available K to L are precisely what the X industry needs. Hence, at first, the output of Y will not fall by very much even as the output of X expands.

If the process continues, however, at some point as Y continues to contract it will begin to layoff larger amounts of L relative to the K it releases. Losing this combination of factors will produce large falls in the output of Y. Yet this ratio of factors is not ideal for X, so its output will increase more slowly.

This may seem difficult, but this is essential preparation for the material in Chapter 4.

10. Why are relative prices more important for decisions about consumption and production than nominal prices? Provide an example to illustrate your answer.

Relative prices are more important than nominal prices because they are more informative to both producers and consumers. That is, they provide these groups with complete information about the degree to which economic conditions have changed. Your examples will vary, but should illustrate how relative prices convey information on opportunity costs.

11. Suppose that a small, tropical country (Home) produces mangoes for domestic consumption and possibly for export. The national demand and supply curves for mangoes in this country are given by the following:

P = 50 - M     (national demand)

P = 25 + M    (national supply)

where P denotes the relative price of mangoes and M denotes the quantity of mangoes (in metric tons).

a) Illustrate these relationships geometrically.

b) What is the autarky price and quantity exchanged?

c) Suppose that the world price of mangoes is 45. Will this small country export mangoes? If so, how many tons?

a) Here's the graph. Note that the y axis shows the  price variable. The units on the y axis should be, say, euros per metric ton of mangoes. The x axis shows the quantity of mangoes. Its units should be metric tons per year.Mango Mkt

b) To find the autarky prices and quantities, the demand and supply equations must be solved simultaneously. To find M, set the right hand sides equal to each other and solve for M. This yields M=12.5 -- Substitute this value into either equation to find P=37.5 -- Alternatively, if your graph is precise, you may read the coordinates of the point where demand crosses supply.

c) Note that this country will export mangoes if the world price is 45. To calculate the amount of exports, construct an export supply equation, also known as excess supply, XS. Algebraically, this is done by subtracting demand from supply:

XS = NS - ND = P - 25 - (50 - P) = 2P - 75.

Now substitute the world price (45) for P, yielding exports of 15 metric tons.

Alternatively, one could substitute 45 for P in both NS and ND, and solve each for M, yielding  20 metric tons of domestic production and 5 metric tons demanded, for an exportable surplus of 15 metric tons. If you draw a horizontal line at P = 45, then you may read these quantities from the demand and supply diagram.

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