Home is a small open economy with perfect capital mobility, and it can be described by the following set of equations: Full-employment level of output:Y FE =5 K 0.25 L 0.75 Stock of capital:K=20736Labour supply:L=10000Consumption:C=8000+0.8(Y−T)−1000rInvestment:I=16500−1500r(Income) Taxes:T=9500Net exports:NX(ε)=6000−200ε, whereε=the real FC/DC exchange rate Money supply:MS=30000Real money demand:L(r+π e ,Y)=0.15Y−300(r+π e )Expected inflation rate:π e =0%Foreign price level:P ∗ =2Note: Real interest rate,r, is expressed in percentage points. For example, ifr=10, thenris10%. Keep your answer to3 decimal points if necessary. a) Suppose the government of Home runs a balanced budget and the world interest rate is5%, find the long-run equilibrium levels of output, net exports, real exchange rate, nominal exchange rate, and price level in Home. (10 points) b) If households grow more pessimistic about the future and opt to save for potential challenging times, this results in a10%change in autonomous consumption. Redo part (a). ( 8 points) c) If the government of Home finds the change in the real exchange rate in part (b) undesirable and wants to keep it to the initial level (i.e., the one in part a) by adjusting its spending on final products, find the level of government spending that will achieve this goal. What happens to the budget balance (i.e., increase/decrease/no change, and by how much)? (7 points)
Question
Home is a small open economy with perfect capital mobility, and it can be described by the following set of equations: Full-employment level of output:Y FE =5 K 0.25 L 0.75 Stock of capital:K=20736Labour supply:L=10000Consumption:C=8000+0.8(Y−T)−1000rInvestment:I=16500−1500r(Income) Taxes:T=9500Net exports:NX(ε)=6000−200ε, whereε=the real FC/DC exchange rate Money supply:MS=30000Real money demand:L(r+π e ,Y)=0.15Y−300(r+π e )Expected inflation rate:π e =0%Foreign price level:P ∗ =2Note: Real interest rate,r, is expressed in percentage points. For example, ifr=10, thenris10%. Keep your answer to3 decimal points if necessary. a) Suppose the government of Home runs a balanced budget and the world interest rate is5%, find the long-run equilibrium levels of output, net exports, real exchange rate, nominal exchange rate, and price level in Home. (10 points) b) If households grow more pessimistic about the future and opt to save for potential challenging times, this results in a10%change in autonomous consumption. Redo part (a). ( 8 points) c) If the government of Home finds the change in the real exchange rate in part (b) undesirable and wants to keep it to the initial level (i.e., the one in part a) by adjusting its spending on final products, find the level of government spending that will achieve this goal. What happens to the budget balance (i.e., increase/decrease/no change, and by how much)? (7 points)
Solution
The question you've asked is quite complex and requires a detailed understanding of macroeconomics. Here's how you can solve it:
a) To find the long-run equilibrium levels of output, net exports, real exchange rate, nominal exchange rate, and price level in Home, you need to solve the system of equations given.
First, we know that in the long run, output equals full-employment output. So, we can substitute the given values into the full-employment output equation to find:
Y_FE = 5 * K^0.25 * L^0.75 = 5 * (20736)^0.25 * (10000)^0.75 = 50000
Next, we can substitute Y_FE and the given tax level into the consumption equation to find the equilibrium level of consumption:
C = 8000 + 0.8 * (Y_FE - T) - 1000 * r = 8000 + 0.8 * (50000 - 9500) - 1000 * 0.05 = 36800
Then, we can substitute Y_FE into the investment equation to find the equilibrium level of investment:
I = 16500 - 1500 * r = 16500 - 1500 * 0.05 = 15750
We can then use the equilibrium condition that Y = C + I + G + NX to find the equilibrium level of net exports:
NX = Y - C - I - G = 50000 - 36800 - 15750 - 9500 = -11050
Next, we can substitute NX into the net exports equation to find the equilibrium real exchange rate:
6000 - 200 * ε = -11050 ε = (6000 + 11050) / 200 = 85.25
The nominal exchange rate is the real exchange rate times the ratio of the foreign price level to the domestic price level. Since we don't have information about the domestic price level, we can't find the nominal exchange rate.
Finally, we can use the money market equilibrium condition that MS = L(r + π_e, Y) to find the price level:
30000 = 0.15 * Y - 300 * (r + π_e) P = MS / L = 30000 / (0.15 * 50000 - 300 * 0.05) = 1.333
b) If autonomous consumption decreases by 10%, the new level of consumption is 0.9 * 8000 = 7200. You can then repeat the steps in part (a) to find the new equilibrium levels.
c) To keep the real exchange rate at the initial level, the government can adjust its spending. You can use the equation for net exports to find the new level of government spending that will make net exports equal to their initial level. The change in the budget balance is the difference between the new level of government spending and the initial level.
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