prelim2solutions

# prelim2solutions - Prelim II Solutions 1.) Consider an...

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Prelim II Solutions 1.) Consider an economy with an aggregate production function y = Ak 1 2 . Depreciation is ten percent, population growth is zero and workers save 1 4 of their income. Productivity is constant and equal to one. a.) Solve for the steady state value of capital stock. k ss is the solution to sAk α = ( n + d ) k . Here, α = 1 2 , A = 1, s = 1 4 , d = 1 10 , and n = 0, so 1 4 k 1 / 2 = 1 10 k 5 2 = k 1 / 2 k ss = 25 4 b.) Solve for the steady state value of per capita output. y ss = Ak α ss , y ss = ( 25 4 ) 1 / 2 = 5 2 c.) Solve for the steady state value of per capita consumption. Consumption is always given by (1 - s ) f ( k ) , c ss = 3 4 5 2 = 15 8 . d.) Solve for the Golden Rule capital stock. k GR solves d dk ± Ak α - ( n + d ) k ² = 0 1 2 k - 1 / 2 = 1 10 5 = k 1 / 2 k GR = 25 e.) If A increases by 2% each year, what is the growth rate of steady state capital per worker? Going back to part a, if we don’t plug in a value for productivity, we get 1 4 Ak 1 / 2 = 1 10 k 5 2 A = k 1 / 2 k ss = 25 4 A 2 If A t +1 = (1 . 02) A t , then A 2 t +1 = (1 . 0404) A 2 t , so k ss will grow by 4 . 04% each year. f.) If A increases by 2% each year, what is the growth rate of steady state output per worker? From above, we have k ss = 25 4 A 2 , so y ss = A ( 25 4 A 2 ) 1 / 2 = 5 2 A 2 , and y ss will grow by 4 . 04% a year. 1

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Grading: Using endogeneous growth theory on e and f also received full credit. If you tried to solve parts e and f using growth accounting, you got half credit on both e and f. It’s not possible to solve this using growth accounting because you only two unknowns, but only one equation. Points were not subtracted for math errors if I was able to determine that you made a math error (if you got a number wrong, but wrote down the correct equation). 2.) Assume that the short run levels of output and the real interest rate are determined by G and T . In the short run, the intersection of the IS and LM curves needn’t be at full employment output. Treat M s and P as ﬁxed, and solve for Y and r in terms of G and T . IS : r = a + G - sY - (1 - s ) T LM : r = fY - M s P a.) What is the short run eﬀect of an increase in balanced budget government spending on Y and r (increase, decrease, no change)? An increase in government spending will shift the IS curve to the right, increasing the short run output and interest rate.
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## This note was uploaded on 09/03/2009 for the course ECON 3140 taught by Professor Mbiekop during the Spring '07 term at Cornell University (Engineering School).

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prelim2solutions - Prelim II Solutions 1.) Consider an...

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