Question

An open economy has the following information on its Income and Expenditures of a given year: The Consumption, Investment and Net Export Functions for the economy are as follows: Consumption, C =500+0.4(Y-T) Investment, I = 450-25r r= r* = 3 percent (please do not convert it into a decimal) Net Export, NX = 500-250ε The economy experienced the following output level with the given Taxes collected and Government Purchases during a given period. Total Income (Real GDP), Y = $2000 Billion Taxes collected, T = $400 Billion Government Purchases, G = $300 Billion

a. Please calculate the private savings, public savings, the national savings, investment, net export and the equilibrium exchange rate.

b. Suppose the government would have increased its spending by 30%. What would have been the equilibrium exchange rate?

Answer 1

(a) At equilibrium ; Y = C + I + G + NX

=> Y = 500 + 0.4(Y-T) + 450 - 25r + 300 + 500 - 250ε

=> Y = 500 + 0.4(Y - 400) + 450 - 25(3) + 300 + 500 - 250ε

=> Y = 1750 + 0.4Y - 160 - 75 - 250ε

=> Y - 0.4Y = 1515 -250ε

=> 0.6Y = 1515 - 250ε

=> 0.6(2000) = 1515 - 250ε

=> 1200 = 1515 -250ε

=> 250ε = 1515 - 1200

=> 250ε = 315

=> ε = (315 / 250)

=> ε =1.26

Thus, equilibrium exchange rate is 1.26

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C = 500 + 0.4(Y-T)

=> C = 500 + 0.4(2000 -400)

=> C = $1140 billion.

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Private saving = Y - C - T

=> Private saving = 2000 - 1140 - 400

=> Private sving = $460 billion

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Public saving = T - G

=> Public saving = 400 - 300

=> Public saving = $100 billion

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National saving = Private saving + Public saving

=> National Saving = $460 billion + $100 billion

=> National saving = $560 billion.

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I = 450 - 25r

=> I = 450 - 25(3)

=> I = $375 billion

=> Investment = $375 billion

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NX = 500 - 250ε

=> NX = 500 - 250(1.26)

=> NX = $185 billion

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(b) Government increased its spending by 30%.

=> New G = $300 billion (1+0.3)

=> New G = $390 billion

At equilibrium ; Y = C + I + G + NX

=> Y = 500 + 0.4(Y-T) + 450 - 25r + 390 + 500 - 250ε

=> Y = 500 + 0.4(Y - 400) + 450 - 25(3) + 390 + 500 - 250ε

=> Y = 1840 + 0.4Y - 160 - 75 - 250ε

=> Y - 0.4Y = 1605 -250ε

=> 0.6Y = 1605 - 250ε

=> 0.6(2000) = 1605 - 250ε

=> 1200 = 1605 -250ε

=> 250ε = 1605 - 1200

=> 250ε = 405

=> ε = (405 / 250)

=> ε =1.62

Thus, new equilibrium exchange rate is 1.62

Equilibrium exchange rate would increase from 1.26 to 1.62