Chapter 11: Problem 8

Table 11.8 represents the data behind a Keynesian cross diagram. Assume that the tax rate is 0.4 of national income; the MPC out of the after-tax income is 0.8; investment is $\$ 2,000 ;$ government spending is $\$ 1,000 ;$ exports are $\$ 2,000$ and imports are 0.05 of after-tax income. What is the equilibrium level of output for this economy?

Short Answer

Expert verified

The equilibrium level of output for this economy is approximately $9090.91$.

Step by step solution

Determine the disposable income

To find the disposable income (DI), we need to consider the tax rate. Given that the tax rate is 0.4 of national income (Y), the equation for disposable income (DI) can be expressed as: DI = (1 - 0.4)Y = 0.6Y

Calculate the consumption function

The consumption function (C) is given by the MPC (marginal propensity to consume) multiplied by the disposable income (DI). We are given that MPC is 0.8. So, the consumption function can be calculated as: C = 0.8 x DI = 0.8 x 0.6Y = 0.48Y

Calculate the import function

The import function (M) is given as a proportion of the disposable income, which is 0.05. M = 0.05 x DI = 0.05 x 0.6Y = 0.03Y

Determine the aggregate demand function

The aggregate demand (AD) function can be found by summing the consumption function (C), the government spending (G), the investment (I), the exports (X), and subtracting the import function (M). We are given G = 1000, I = 2000, and X = 2000. So, we can write the AD function as: AD = C + I + G + X - M = 0.48Y + 2000 + 1000 + 2000 - 0.03Y Combining the terms with Y, we get: AD = (0.45Y) + 5000

Determine the aggregate supply function

In the Keynesian cross model, the aggregate supply function is equal to national income: AS = Y

Find the equilibrium level of output

The equilibrium level of output is the point where aggregate demand equals aggregate supply: AD = AS 0.45Y + 5000 = Y Now, solve for Y: 0.55Y = 5000 Y = 5000 / 0.55 Y = 9090.91 The equilibrium level of output for this economy is approximately $9090.91.