Macro Module 4 Solow growth model savings rate practice exam questions

Countries ABC and XYZ follow the simple Solow growth model, with no changes in the technology level.

●    The savings rate is 31% greater in country ABC than in country XYZ.
●    The depreciation rate is 5.34% and the population growth rate is 2.80% in both countries.
●    In 20XX, capital per worker is 836 and real GDP per worker is 266 in both countries.
●    The growth rate of capital per worker in country XYZ is 1.35% per annum.

Question 4.1: Ratio of income to capital

What is the ratio of income to capital in 20XX for these two countries?

Answer 4.1: 266 / 836 = 31.82%


Question 4.2: Savings rate

What is the savings rate in country XYZ?

Answer 4.2: (2.80% + 1.35%) / (31.82% – 5.34%) = 15.67%

growth rate of capital per worker = savings rate × (ratio of income to capital – depreciation rate) – population growth rate ➾

savings rate = (population growth rate + growth rate of capital per worker) / (ratio of income to capital – depreciation rate)


Question 4.3: Savings rate

What is the savings rate in country ABC?

Answer 4.3: 15.67% × (1 + 31%) = 20.53%

(savings rate is 31% higher in ABC than in XYZ)


Question 4.4: Growth rate of capital per worker

What is the growth rate of capital per worker in country ABC?

Answer 4.4: 20.53% × (31.82% – 5.34%) – 2.80% = 2.64%

(growth rate of capital per worker = savings rate × (ratio of income to capital – depreciation rate) – population growth rate)