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Unformatted text preview: The Theory of Economic Growth Problem set 1 Solutions ¨ Omer ¨ Ozak * September 24, 2008 Towards the end of the 16th century potatoes are introduced to Ireland and within a short time period they became the prime agricultural crop in Ireland. Suppose Ireland is in a Malthusian steadystate equilibrium prior to the 16th century. Problem 1. Establish formally its Malthusian steady state level of income and population. Solution: Remember that in the Malthusian model, the level of income in period t is determined by the equation Y t = ( A 1 X ) α L 1 α t where Y t is the level of income, A 1 the level of technology, X the amount of land available and L t the number of workers. Define the level of income per worker as y t ≡ Y t L t = parenleftbigg A 1 X L t parenrightbigg α . Households, in this case Irish ones, are assumed to decide the number of children and the amount of consumption they want to have. 1 An individual in her second period of life in period t takes this decision by solving the following problem: max s.t....
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 Fall '08
 GALOR
 Steady State, steady state level

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