econ151a_ps7_solutions

econ151a_ps7_solutions - Problem Set 7 Solutions 1.a IF...

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Problem Set 7 Solutions 1.a. IF immigrants and natives are perfect substitutes, an influx of immigrants will reduce wages in the short-run. Supply shifts from S0 to S1, and wage falls from W0 to W1 b. If capital is mobile and can adjust in the long-run, and labor is mobile, the effect of immigration on wages will disappear in the long run. First, with mobile capital, the initial increase in labor supply from immigration, and lowered wage, will encourage more capital to enter this market. This can be seen most easily by taking a simple Cobb-Douglas production function, and noting that in the long run all factor must be set so that the value of their marginal product is equal to the factor price. Start with a production function given by: q(L,K) = AK α L 1- α , (0< α < 1, CRS), then profit maximization implies r =p α A(K/L) α -1 w=p(1- α )A (K/L) α Since these two equations have to hold, if L increases (from immigration), r must rise (capital is now more valuable in production because there are more workers around to use it). The increase in r will eventually attract more capital into this market.
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