8~9. Use the following information to solve two questions.
C = 100 + 0.8Yd (Consumption), I = 200 –1,000i (Investment) L = Y – 10,000i (Money Demand) G = 550, T = 500, Ms = 900, Yd = Y – T
8. Find the equilibrium level of Y, I, C and interest rate (i).
9. Suppose the independent investment is decreased up to 90 from 200. (A) Find the new equilibrium level of Y, C and i. (B) How much does Bank of Korea change the money supply to get the initial level of GDP?
To find the equilibrium level of Y, I, C, and interest rate (i), we need to use the given equations and information.
8. Equilibrium level of output (Y) is determined by the condition that Y = C + I + G, where C is consumption, I is investment, and G is government spending. Putting the given information into the equation, we have:
Y = (100 + 0.8Yd) + (200 – 1,000i) + 550
Next, we need to find the disposable income (Yd) using the equation Yd = Y – T. Given T = 500, we can substitute it in the equation:
Yd = Y – 500
Now, we can substitute Yd into the consumption equation C = 100 + 0.8Yd:
C = 100 + 0.8(Y – 500)
Expanding and simplifying the equation, we get:
C = 100 + 0.8Y – 400
C = 0.8Y – 300
Substituting the values of Y, C, and G into the output equation, we get:
Y = (0.8Y – 300) + (200 – 1,000i) + 550
Simplifying further:
Y = 0.8Y – 300 + 200 – 1,000i + 550
Rearranging terms:
0.2Y - 1,000i = 1,050
Now, we have two equations to solve simultaneously:
Y = 0.8Y - 300 + 750
0.2Y - 1,000i = 1,050
Simplifying the first equation, we get:
0.2Y = 450
Y = 2,250
Substituting Y = 2,250 into the second equation:
0.2(2,250) - 1,000i = 1,050
450 - 1,000i = 1,050
-1,000i = 600
i = -0.6
Therefore, the equilibrium level of output (Y) is 2,250, investment (I) is 200, consumption (C) is 1,750, and the interest rate (i) is -0.6.
9.
(A) To find the new equilibrium level of Y, C, and i when independent investment decreases from 200 to 90, we use the same equations as before but substitute the new investment value:
New Y = (0.8Y - 300) + (90 - 1,000i) + 550
Simplifying further:
New Y = 0.8Y - 300 + 90 - 1,000i + 550
Rearranging terms:
0.2Y - 1,000i = 340
Now, we have two equations to solve simultaneously:
New Y = 0.8Y - 300 + 640
0.2Y - 1,000i = 340
Simplifying the first equation, we get:
0.2Y = 940
New Y = 4,700
Substituting New Y = 4,700 into the second equation:
0.2(4,700) - 1,000i = 340
940 - 1,000i = 340
-1,000i = -600
i = 0.6
Therefore, the new equilibrium level of output (New Y) is 4,700, consumption (C) is 1,940, and the new interest rate (i) is 0.6.
(B) To find how much the Bank of Korea needs to change the money supply (Ms) to get the initial level of GDP, we need to consider the money demand (L) equation L = Y - 10,000i and the fact that the money supply (Ms) is currently 900.
For the initial level of GDP, the equation becomes:
900 = Y - 10,000(0.6)
Simplifying:
900 = Y - 6,000
Y = 6,900
Therefore, the Bank of Korea needs to change the money supply (Ms) by 6,900 - 900 = 6,000 to get the initial level of GDP.