Partial Answer Key



Partial Answer Key

Comparing GDP Using Purchasing Power Parity

1) Consider two economies, Richania and Pooristan, which produce and consume only bread and buildings. The table contains price and production data for each country:

|Country |Bread Produced per Capita|Buildings Produced per |Price of Bread in Local |Price of Buildings in |

| | |Capita |Currency |Local Currency |

|Richania |90 |30 |4 |100 |

|Pooristan |15 |5 |2 |10 |

a. Calculate the level of GDP per capita in each country, measured in its own currency.

Richania: 90*4 + 30*100 = 3360 Richanian dollars (R$)

Pooristan: 15*2 + 5*10 = 80 Pooristanian dollars (P$)

b. Calculate the market exchange rate between the currencies of the two countries.

2 R$/1 P$ (look at traded good prices for this rate)

c. What is the ratio of GDP per capita in Richania to GDP per capita in Pooristan, using the market exchange rate?

80 P$ * (2 R$/1 P$) = 160 R$. This calculation implies that Richania is

(3360 R$/160 P$) = 21 times wealthier than Pooristan.

d. Calculate the purchasing power parity (PPP) exchange rate between the two currencies.

The basket of goods should be 3 units of bread and one building.

Richania: 3*4 R$ + 1*100 R$ = 112 R$

Pooristan: 3*2 P$ + 1*10 P$ = 16 P$

Thus the PPP exchange rate is 112 R$/16 P$ = 7 R$/1 P$

e. What is the ratio of GDP per capita in Richania to GDP in Pooristan, using the PPP exchange rate?

80 P$ * (7 R$/1 P$) = 560 R$. This calculation implies that Richania is

(3360 R$/560 P$) = 6 times wealthier than Pooristan.

Computing Growth Rates

2) Suppose x grows at 5% per time period (that is, xt = 1.05t), and y grows at 2% per time period (that is, yt = 1.02t). Calculate the growth rate of z in each of the following cases:

a. z = xy 0.05 + 0.02 = 0.07

b. z = x/y 0.05 – 0.02 = 0.03

c. z = y/x 0.02 – 0.05 = -0.03

d. z = x1/2y1/2 (0.5*0.05) + (0.5*0.02) = 0.035

e. z = (x/y)2 (2*0.05) - (2*0.02) = 0.06

f. z = x-1/3y2/3 (-0.33*0.05) + (0.67*0.02) = -0.33

How Do We Know Growth Over the Very Long Run?

3) The poorest countries in the world have a per capita income of about $600 today. We can reasonably assume that it is nearly impossible to live on an income below half this level (below $300). Per capita income in the United States in 2000 was about $33,000. With this information in mind, consider the following questions.

a. For how long is it possible that per capita income in the United States has been growing at an average annual rate of 2% per year?

300 * (1.02)t = 33,000. Solve for t to get t = ln(110)/ln(1.02) = 237.4 years

b. Some economists have argued that growth rates are mis-measured. For example, it may be difficult to compare per capita income today with per capita income a century ago when so many of the goods we can buy today were not available at any price then. Suppose the true growth rate in the last century was 3% per year rather than 2%. What would the level of per capita income in 1800 have been in this case? Is this answer plausible?

For the twentieth century: x * (1.03)100 = 33,000

For the nineteenth century: y * (1.02)100 = x

So, first solve for x (the implied income for 1900), and then use this to solve for y (the implied income for 1800). You should get y = 237 bucks. The answer is thus implausible if we believe mankind cannot survive on less than 300 dollars (valued today). In other words, twentieth century growth could not have been that rapid.

Cobb-Douglas and Payments to the Factors of Production

4) Suppose that the production function is represented by the Cobb-Douglas function:

[pic].

a. What fraction of income do capita and labor receive?

Capitalists get one tenth of it, laborers get nine tenths of it. Yes, you can just look at the exponents, but you should also be able to “prove” this.

b. Suppose immigration raises the labor force by 10 percent. What happens to total output (in percentage terms)? The real rental price of capital (in percentage terms)? The real wage (in percentage terms)?

First, note that MPK = [pic], and that

MPL = [pic]

So, when L rises by a factor of 1.1, Y rises by (1.1)9/10 = 8.96%.

Rental price of capital = MPK rises by (1.1)9/10 = 8.96%.

Real wage of labor = MPL falls by (1.1)-1/10 = 0.0095, or a 0.95% decrease.

c. Suppose the World Bank gives aid to a country that raises its capital stock by 10 percent. What happens to total output (in percentage terms)? The real rental price of capital (in percentage terms)? The real wage (in percentage terms)?

Y rises by (1.1)1/10 = 0.96%.

MPK falls by (1.1)-9/10 = 0.918, or an 8.2% decrease.

MPL rises by (1.1)1/10 = 0.96%.

d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to total output (in percentage terms)? The real rental price of capital (in percentage terms)? The real wage (in percentage terms)?

Note that the technological coefficient has no exponent on it (think about why that is). So output, MPK and MPL all rise by 10%.

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