Given the following Keynesian model:
$\begin{array} { c l }
\mathrm { Y } = \mathrm { C } + \mathrm { I } + \mathrm { G } + \mathrm { X } - \mathrm { M } & \mathrm { I } = 250 \
\mathrm { C } = 80 + 0.75 \mathrm { Y } _ { \mathrm { d } } & \mathrm { G } = 100 \
\mathrm { Y } _ { \underline { d } } = \mathrm { Y } - \mathrm { T } & = 200 \
\hline \mathrm { T } = 0.20 \mathrm { Y } & \mathrm { M } = 0.30 \mathrm { Y }
\end{array}$
(a) Calculate the equilibrium level of income and indicate the value of the current account balance when the economy is at its equilibrium income level.
(b) Suppose that all equations in the model above stay the same except the size of exports. Calculate the level of exports needed to yield an equilibrium income level that also has X = M, and indicate that resulting equilibrium income level.

Question

Given the following Keynesian model:
$\begin{array} { c l } 
\mathrm { Y } = \mathrm { C } + \mathrm { I } + \mathrm { G } + \mathrm { X } - \mathrm { M } & \mathrm { I } = 250 \
\mathrm { C } = 80 + 0.75 \mathrm { Y } _ { \mathrm { d } } & \mathrm { G } = 100 \
\mathrm { Y } _ { \underline { d } } = \mathrm { Y } - \mathrm { T } & = 200 \
\hline \mathrm { T } = 0.20 \mathrm { Y } & \mathrm { M } = 0.30 \mathrm { Y }
\end{array}$
(a) Calculate the equilibrium level of income and indicate the value of the current account balance when the economy is at its equilibrium income level.
(b) Suppose that all equations in the model above stay the same except the size of exports. Calculate the level of exports needed to yield an equilibrium income level that also has X = M, and indicate that resulting equilibrium income level.

Quizplus · Accepted Answer

The Answer is To solve for the equilibrium level of income (Y) and the current account balance, we need to use the information given in the Keynesian model.

(a) Calculate the equilibrium level of income and indicate the value of the current account balance when the economy is at its equilibrium income level.

First, we need to express all the components of the model in terms of Y:

1. Consumption (C) is given as C = 80 + 0.75Yd, where Yd is disposable income.
2. Investment (I) is given as I = 250.
3. Government spending (G) is given as G = 100.
4. Taxes (T) are given as T = 0.20Y.
5. Imports (M) are given as M = 0.30Y.

Disposable income (Yd) is Y - T, so we can write it as Yd = Y - 0.20Y = 0.80Y.

Now we can substitute Yd into the consumption function:
C = 80 + 0.75(0.80Y) = 80 + 0.60Y.

The equilibrium condition in a Keynesian model is that aggregate demand (AD) equals aggregate output (Y), so we can write the equilibrium condition as:
Y = C + I + G + X - M.

Substituting the expressions for C, I, G, and M into the equilibrium condition, we get:
Y = (80 + 0.60Y) + 250 + 100 + X - (0.30Y).

Now we need to solve for Y. First, let's simplify the equation by combining like terms:
Y = 80 + 0.60Y + 250 + 100 + X - 0.30Y
Y = 430 + X + 0.60Y - 0.30Y
Y = 430 + X + 0.30Y.

Now, we isolate Y on one side of the equation:
Y - 0.30Y = 430 + X
0.70Y = 430 + X.

To find the equilibrium level of income (Y), we need to know the value of exports (X). However, X is not given in the problem. Assuming that the economy is in equilibrium and that X = M, we can substitute M for X in the equation:
0.70Y = 430 + 0.30Y.

Now we solve for Y:
0.70Y - 0.30Y = 430
0.40Y = 430
Y = 430 / 0.40
Y = 1075.

So the equilibrium level of income (Y) is 1075.

To find the current account balance, we need to calculate the difference between exports (X) and imports (M) at the equilibrium level of income. Since we assumed X = M for equilibrium, the current account balance is zero.

(b) Suppose that all equations in the model above stay the same except the size of exports. Calculate the level of exports needed to yield an equilibrium income level that also has X = M, and indicate that resulting equilibrium income level.

We have already assumed X = M to find the equilibrium level of income in part (a), and we determined that Y = 1075. To find the level of exports (X) that would yield this equilibrium income level with X = M, we use the import function:

M = 0.30Y
M = 0.30 * 1075
M = 322.5.

Since we want X = M for equilibrium, the level of exports needed is also 322.5. Thus, the resulting equilibrium income level is 1075, with exports (X) and imports (M) both equal to 322.5.

Given the Following Keynesian Model (A) Calculate the Equilibrium Level of Income and Indicate the \mathrm

Given the Following Keynesian Model (A) Calculate the Equilibrium Level of Income and Indicate the
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