Question

1. Consider a country that is initially in steady state. Suppose the saving rate increases. Moreover, the population growth rate increases by 1% but the capital depreciation rate falls by 1%. According to the Solow–Swan model, the per capita capital stock increases, and the country moves to a new, higher steady state level of per capita income.

Answer true, false, or uncertain. Please briefly explain your answer.

2.

Consider the country of Solow, which is described by the Solow–Swan model. Let the saving rate θ = 0.8; let the population growth rate n = 0.05; let the rate of depreciation d = 0.05. If per capita income y = 100 and the per capita capital stock k = 1000, which of the following is true?

a) Replacement investment is 100, saving is 80 and k will increase towards the steady state per capita capital stock

b) Replacement investment is 100, saving is 60 and k will decrease towards the steady state per capita capital stock

c) Replacement investment is 100, saving is 80 and k will decrease towards the steady state per capita capital stock

d) Replacement investment is 100, saving is 80 and k is at the steady state per capita capital stock

3.

Consider the country of Solow, which is described by the Solow–Swan growth model with constant total factor productivity. Let the saving rate θ = 0.75. Per capita output (y) is equal to 100 and the per capita capital stock (k) is 1000. For Solow to be in steady state:

a) the depreciation rate is 0.025 and the population growth rate is 0.05
b) the depreciation rate is 0.25 and the population growth rate is 0.5
c) the sum of the depreciation rate and the population growth rate must be less than 0.075

d) the depreciation rate and population growth rate must sum to 0.75

Answer 1

Q1) The answer is true. Since the increase in population growth rate and decrease in depreciation is the same, they cancel out in terms of change in the replacement investemnt. But since savings has increased, the economy Willa accumulate more capital per worker and move to a higher steady state of per capita income.

Q2) The answer is (c)

savings = sy = 0.8*100 = 80

Replacement investment = (0.05 +0.05)*100 = 0.1*1000 = 100

Since, replaceent investment is greater than savings, capotal per worker will decrease and move towards the per-capita steady state capital stock

Q3) The answer is (a)

Savings = 0.75*100 = 75

Replacement investment = (depreciation rate + growth rate)*1000

At steady state, (depreciation rate + growth rate)*1000 = 75

=> (depreciation rate + growth rate) = 75/1000 = 0.075

This is happening in (a) as 0.025 + 0.05 = 0.075

All other options are incorrect as they will not lead to a Solow steady state.