Assume that initially the IS curve is given by IS1: Y = 12-1.5T-30i+2G, and that the price level P is
1, and the LM curve is given by LM1: M= Y(1-i). Initially, the home interest rate equals the foreign interest rate of 10% or 0.1. Taxes and
government spending both equal 2.
-I found the output is 10 (this is the desired output)
There is now a foreign demand shock, such that the IS curve shifts left by 1.5 units at all levels of the
interest rate, and the new IS curve is given by IS2: Y = 10.5-1.5T-30i+2G.
Assume that the central bank refuses to change the interest rate from 10%. In this case, what is the new level of output? What is the money supply? And if the government decides to use fiscal policy instead to stabilize output (to desired output=10), then, according to the new IS curve, by how much must government spending be increased to achieve this goal?
I don't get the part where it says assume central refuses to change interest from 10%, but when your IS curve shifts, won't interest decrease?
When the statement says "assume the central bank refuses to change the interest rate from 10%," it means that they are not adjusting the interest rate in response to the foreign demand shock. In reality, the interest rates might change due to various factors, but for the purpose of this scenario, we are assuming that the interest rate remains fixed at 10%.
Now, let's analyze the effects of the foreign demand shock on the new level of output:
1. New Level of Output: The new IS curve, IS2, is given by Y = 10.5 - 1.5T - 30i + 2G. With the interest rate remaining at 10%, we can substitute this value into the equation to find the new level of output.
Y = 10.5 - 1.5T - 30(0.1) + 2G
Y = 10.5 - 1.5T - 3 + 2G
Y = 7.5 - 1.5T + 2G
By replacing the interest rate with its fixed value, we obtain the new IS equation. Now we can substitute the given values of T (taxes) and G (government spending) to find the new level of output.
Assuming taxes (T) and government spending (G) both equal 2, we have:
Y = 7.5 - 1.5(2) + 2(2)
Y = 7.5 - 3 + 4
Y = 8.5
Therefore, the new level of output is 8.5.
2. Money Supply: The money supply is not directly influenced by the foreign demand shock or the IS-LM model. The LM curve, LM1: M = Y(1-i), remains unchanged. Thus, the money supply (M) is determined by the level of income (Y) and the interest rate (i). In this scenario, the LM curve does not shift, so the money supply remains the same as before.
3. Fiscal Policy: To stabilize output at the desired level of 10, the government needs to adjust its spending (G). We can use the new IS curve, IS2: Y = 10.5 - 1.5T - 30i + 2G, to calculate the change in government spending required.
10 = 10.5 - 1.5T - 30(0.1) + 2G
10 = 10.5 - 1.5T - 3 + 2G
10 - 10.5 + 3 = -1.5T + 2G
2.5 = -1.5T + 2G
By rearranging the equation, we can isolate the change in government spending (ΔG) needed to achieve the desired output:
ΔG = 2.5 + 1.5T
Substituting T = 2 (given in the scenario), we find:
ΔG = 2.5 + 1.5(2)
ΔG = 2.5 + 3
ΔG = 5.5
Therefore, the government needs to increase spending by 5.5 to stabilize output at the desired level of 10.