1. In this question you will derive the Harrod-Domar growth equation (including population growth) and explore the possibility of a "growth trap".

a) First, write down the aggregate capital accumulation equation. [7 marks]

b) From there, derive the Harrod-Domar formula for growth in outputper-capitaas a function of the savings rate (s), the capital-output ratio (), the rate of depreciation (), and the population growth rate (n). [8 marks]

For the rest of this problem, imagine a country in which the savings rate is 20%, the capital-output

ratio is 4 and the rate of depreciation is 2%.

c) If the population growth rate is 2%, what will the per-capita growth rate be - according to the Harrod-Domar growth equation? [3 marks]

d) It is generally observed that poorer countries have much higher fertility rates (and thus population growth rates) than rich countries. In particular, let's say that the relationship between the population growth rate (n) and income per capita (y, measured in thousands of dollars) is described by the following formula:n=.1y+ 6.Find and graphthe relationship betweengrowth inGDP per capita (g) and income per capita (y). Recall thatyis measured in thousands of dollars, soy= 15refers to an income per capita of$15,000. [7 marks]

e) Interpret the graph from part d) above. What conclusions can you draw from it regarding growth dynamics of poor versus rich countries? [10 marks]