Final answer:
The equilibrium output and income in the given closed economy, using the Keynesian cross model, is 1100. This is found by setting the planned aggregate expenditure equal to output and solving for the output (Y), which in this case accounts for consumption, investment, and government spending but no taxes.
Step-by-step explanation:
To determine the equilibrium output and income in a closed economy with the provided economic parameters, we use the basic Keynesian cross model. In this model, equilibrium occurs where planned aggregate expenditure equals actual output (Y). The formula for aggregate expenditure (AE) in this economy, which does not collect taxes, is AE = C + I + G, where:
- C is consumption, which is given as C = 250 + 0.50Yd (with Yd = Y since there are no taxes).
- I is intended investment, which is constant at 150.
- G is government spending, which is also constant at 150.
Thus, AE = 250 + 0.50Y + 150 + 150. For equilibrium, we set AE equal to Y:
- Y = 250 + 0.50Y + 150 + 150.
- To solve for Y, we combine like terms and isolate Y:
- Y - 0.50Y = 250 + 150 + 150.
- 0.50Y = 550.
- Y = 1100.
The equilibrium output and income for this closed economy is therefore 1100. This is the level of national income where the amount of goods produced is exactly equal to the amount of goods and services demanded.