Question

Part 1 In 1950 the U.S. had a population of 150 million and it was growing at 1.3% a year. Assume no net migration. (10 points total) a. In about how many years will it take for the U.S. population to double? (5 points) b. In 2010 U.S. population was 308 million. Calculate the average annual growth rate of the population over these 60 years. (5 points) Part 2 In year 1, a country has a population of 100 people; 50 of whom have an income of $20 and the other 50 have an income of $30. In year 2, the higher income group has changed; instead of 50 people earning $30, 30 now earn the same $30 and 20 earn $40. (15 points total) c.Plot the Lorenz curves for both years. (5 points) d. What has happened to income inequality? Why? (5 points) e. Calculate the Gini coefficient for year 1. (5 points) Part 3 The Netherlands is described by the Solow model with a production function y k1/3where y is the output per worker and k is capital per worker. Now, suppose that the fraction of output invested (or saved) is 30%, that the depreciation rate is 30%, and that there is no population growth. (20 points total) f.Calculate the country's steady state level of output per worker. (4 points) Now,say that k is equal to 30. Is the country at its steady-state level of output per worker, above the steady state or below the steady state? Show how you reached your calculations.(4 points) h. Graphically illustrate your answer to f.Also, show how the level of capital in g compares to the steady-state value. (4 points) i. Now, say that population growth rises from 0% to 2%. What would be the resulting value of this country's steady state level of output per worker? (4 points) j. If this country wished to return to the original steady-state level of output per worker (i.e. in part f), what could it do? (4 points) Part 4 k. Consider a family in a developing country whose income rises and how their fertility decisions would be affected by their changed status. Be sure to mention the roles of the income and substitution effects. (5 points)

Answer 1

Part 1.

U.S. Population in 1950 = 150 million

Growth rate = 1.3%

No net migration.

a)

If the population grows at a constant rate annual rate g, the value of its population after t years is given by the following formula:

N-No(1+g)'

We need to find t such that N_t = 2N_o (i.e. original population doubles itself)

Using this in growth population and taking log both sides, we get:

21+0.013) In2-tIn1.013 No In2 53.67 54 years In1.013

b)

Average growth rate =

Final population - Initial population 308- 150 2.63% Total time taken 60