Practice_Problems_2_with_answers - Economics 102 Winter...

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Economics 102, Winter, 2010 Midterm Exam # 2 practice questions Professor Lee Ohanian (1) Show that in the Solow model in which population grows at rate n, that the Golden Rule requires that the marginal product of capital be equal to the sum of the depreciation rate and the growth rate of the population. Why is the golden rule MPK higher for a higher population growth rate? K t +1 = I t + (1 ) K t in per-capita terms we have K t +1 L t = I t L t + (1 ) K t L t This equation can be re-writte as: K t +1 L t +1 L t +1 L t = I t L t + (1 ) K t L t in the new variables is: k t +1 (1 + n ) = i t + (1 ) k t In the steady-state (we drop the time subscripsts) k ( + n ) = i Investment per-capita be written as output minus consumption per-capita k ( + n ) = y c Hence c = y k ( + n ) The optimal condition for the golden rule is when we derive respect to capital @c @k = @y @k ( + n ) If we make the derivative equal to zero (which is the neccesary condition for a maximum) @y @k ( + n ) = 0 MPK = ( + n ) 1
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When n is higher, golden-MPK is higher due to shrinking capital stock per worker, because of higher amount of investment necessary to provide higher number of new workers with capital. k is spreaded thinly among a larger number of workers (2) Show that in the Solow model in which there is constant growth in worker e¢ ciency that a steady state exists for the variable Y= ( NE ) ; and that once the steady state is reached that per capita output grows at rate g: Start with the production function Y = K ( NE ) 1 Divide through NE Y NE = K NE ± NE NE ± 1 y = k where y = Y NE and k = K NE : The law of motion of capital can be re-expressed as: k = i ( + n + g ) k
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This note was uploaded on 03/06/2010 for the course ECON 102 taught by Professor Serra during the Spring '08 term at UCLA.

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Practice_Problems_2_with_answers - Economics 102 Winter...

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