# answerstohomework3spring2005 - Economics 302 Prof Kelly...

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Economics 302 Prof. Kelly Problem Set 3 Answer Key Exercise 1 Open Economy Equilibrium Suppose in the country of Kelly, which is initially closed to the outside world (ie, does not trade with other nations), output is produced in each period using just two factors, capital ( K ) and labor ( L ) under the following production function: Y = F ( K; L ) = 6 K : 5 L : 5 Kelly has a population of one million people; every individual gets an equal share of output; and each individual consumes output according to the following Keynesian consumption function, where y is the output allocated to an individual and t is the tax paid by each individual: c = : 8( y ¡ t ) Every individual in Kelly inelastically supplies one unit of labor and four units of capital for production. We then have that k is the amount of capital provided by each individual and K is the total amount of capital provided for production. Similarly for l and L: The government of Kelly runs a balanced budget and spends two million units of output per period. Every individual faces the same tax. a) What is total ouput in the economy? Y = 6(4 ¤ 1 ; 000 ; 000) : 5 (1 ; 000 ; 000) : 5 = 6 ; 000 ; 000(4) : 5 (1) : 5 = 12 ; 000 ; 000 b) What is the wage rate in the economy w = MPL = (1 ¡ fi ) Y L = : 5 1 ; 000 ; 000 (12 ; 000 ; 000) = 6 c) How much does an individual consume in the economy? c = : 8(12 ¡ 2) = 8 1

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d) What is total investment ( I ) in the economy I = S = Y ¡ G ¡ C = 1 ; 000 ; 000(12 ¡ 2 ¡ 8) = 2 ; 000 ; 000 Now, suppose that we have the following investment function for each individual: i = : 08 r e) Determine what the interest rate is in this economy. i = 2 = : 08 r ) 2 r = : 08 r = : 04 f) What is the interest rate if government spending increases to 3 million units and the government main- tains a balanced budget? What if government spending decreases to 1 million units? G=3,000,000 which implies T=3,000,000 so consumption must be recalculated. c = : 8(12 ¡ 3) = : 8(9) = 7 : 2 I = S = Y ¡ G ¡ C = 1 ; 000 ; 000(12 ¡ 3 ¡ 7 : 2) = 1 ; 800 ; 000 i = 1 : 8 ) 1 : 8 r = : 08 r = : 08 1 : 8 r = : 044 2
G=1,000,000 c = : 8(12 ¡ 1) = : 8(11) = 8 : 8 I = S = Y ¡ G ¡ C = 1 ; 000 ; 000(12 ¡ 1 ¡ 8 : 8) = 2 ; 200 ; 000 i = 2 : 2 ) 2 : 2 r = : 08 r = : 08 2 : 2 r = : 036 g) What happens to the interest rate if government spending increases to 3 million units but does not change the tax to maintain a balanced budget? What happens if government spending decreases to 1 million

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