Suppose that there are only two goods produced in the world

Question

ECON 448: Week 1-

1. Purchasing Power Parity (PPP) Exchange Rates

1. How do we know whether or not a country is richer or poorer than other countries?

2. Problems in simple comparison of GDP between countries.

3. Purchasing Power Parity (PPP) exchange rates: A set of artificial exchange rates which are based on the prices of a standardized basket of goods and services (both traded and nontraded).

4. Exercise 1: The number of people worldwide living on less than one dollar per day can be calculated using either market exchange rates or purchasing power exchange rates. Which will be larger? Explain why.

5. Exercise 2: Suppose that there are only two goods produced in the world: computers, which are traded internationally, and ice cream, which is not. The following table shows information on the production and prices of computers and ice cream in two countries:

Country	Computers Produced per capita	Ice Cream Produced per capita	Price of Computers in Local Currency	Price of Ice Cream in Local Currency
Richland	12	4	2	4
Poorland	3	1	1	1

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

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

(c) What is the ratio of GDP per capita in Richland to GDP per capita in Poorland, using the market exchange rate?

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

(e) What is the ratio of GDP per capita in Richland to GDP per capita in Poorland, using the PPP exchange rate?

2. Exponential Growth and Logged Variables

1. Exponential Growth = Constant Growth Rate

A_t = A₀ × (1 + r)^t

2. Why taking log?

lnA_t = ln[A₀ × (1 + r)^t]

      = lnA₀ + t × ln(1 + r)

      ≈ lnA₀ + t × r

3. Basic Log Rules

(a) log_bxy = log_bx + log_by (x > 0, y > 0)

Caution! log_b(x + y) ≠ log_b(x) + log_b(y)

(b) log_b x/y = log_bx - log_by (x > 0, y > 0)

(c) log_bx^z = z × log_bx (x > 0)

(d) log_b1 = 0

(e) b^log_bx = x (x > 0) (by def!)

(f) log_ex = lnx (e = lim_r→0(1 + r)^1/r = 2.718...)

4. How many years does it take to make GDP doubled when the annual growth rate is r?