In the model of the poverty trap used by Sachs (also known as the Lewis model), Y=min(AK,BL). (where Y is GDP, K is capital stock, L is labor, and A and B are model parameters). Using this model, give an algebraic expression for the minimum amount of aid necessary to exit a poverty trap for a country. The necessary aid should be as a ratio to the recipient’s GDP. Show how this amount depends on the depreciation rate for the capital stock, the population growth rate for the country, the rate of return to capital (A), and the recipient country’s saving rate. Now calculate the required amount of aid if the depreciation rate = .05, the population growth rate =.02, A=0.2, B=0.4, and the saving rate = 0.15. Explain why the country would remain in poverty without this amount of aid. Discuss what assumptions on surplus labor and aid effects are necessary for the model to be correct on how aid is both necessary and sufficient to end the poverty trap. Discuss what the model says about unemployment, including in the case of openness to capital flows.
In the model of the poverty trap used by Sachs (also known as the Lewis model), Y=min(AK,BL). (where Y is
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