Final answer:
To determine the real interest rate that clears the goods market at full employment, we must find the level of national income at equilibrium using the given economic parameters and then determine the interest rate that equates planned investment with savings. Additional information on the investment function in relation to interest rates is needed to find the specific real interest rate.
Step-by-step explanation:
To find the real interest rate that clears the goods market in an economy operating at full employment, we apply the goods market equilibrium condition which is derived from the Keynesian Cross model. In equilibrium, the total production (or real GDP) in the economy is equal to the total aggregate expenditure. The aggregate expenditure is the sum of consumption (C), investment (I), government spending (G), and net exports (X-M). Since the real GDP (Y) equals full-employment output, the equation is simplified to Y = C + I.
Given the economic parameters:
- Y = National income
- T = Taxes = 0.3Y
- C = Consumption = 200+ 0.9(Y – T)
- I = Investment = 600
We can calculate consumption (C) by substituting T with 0.3Y in the consumption function:
C = 200 + 0.9(Y - 0.3Y)
C = 200 + 0.9(0.7Y)
C = 200 + 0.63Y
Now, setting the equilibrium condition Y = C + I, we have:
Y = 200 + 0.63Y + 600
To isolate Y, we solve for Y:
Y - 0.63Y = 800
0.37Y = 800
Y = 800 / 0.37
Y = Approximately 2162.16
Now, since investment (I) is typically responsive to the real interest rate, we would need additional information such as the investment function regarding interest rates to calculate the exact real interest rate that clears the goods market. This real interest rate would be the rate where planned investment corresponds to the level of savings at full-employment output.