Question

Consider the Basic growth model from your text and lecture as defined below: Production function: GDP = f(At, Kt, Lt); where capital (K) and labor (L) are substitutes and technology (A) aids production Demographic Behavior: Lt+1= Lt(1+n) = Nt+1; where n is the population growth rate, N is the total population and there is no unemployment Capital and Savings/Investment Dynamics: Kt+1 = It + Kt(1-?); It = St = s*Y; where ? is the depreciation rate of capital, s is the savings rate and investment is I. Technology Change: At+1= At(1+?); where ? is the constant growth rate of technology. Suppose output would be Y*1 in the next period if nothing changed. Part 3: Remove the minimum consumption constraint, but now suppose that a political crisis in a nearby country leads to a large group of migrants arriving, increasing the population by M people. To model this, alter the basic model such that: Lt+1= Lt(1+n) + M; where M is the number of migrants arriving g) How would the arrival of M immigrants affect the following outcomes? Meaning, will they be larger, smaller, or is it unknown, compared to a world where no migrants arrived? Why (1-2 sentences)? i. GDP ii. GDP per capita Now suppose that the production function f(A,K,L) is such that capital and labor are complements instead of substitutes, and furthermore that the country has a savings rate that is equal to its depreciation rate. h) How would the arrival of M immigrants affect the following outcomes? Why (1-2 sentences)? i. GDP ii. GDP per capita

Answer 1