Final answer:
In the Keynesian cross model, the planned expenditure is equal to the sum of consumption, investment, and government purchases. By solving the equation, we can find the equilibrium income. To calculate the new equilibrium income when government purchases increase, substitute the new value into the equation. The government purchase multiplier can be calculated using the change in equilibrium income and the change in government purchases.
Step-by-step explanation:
In the Keynesian cross model, planned expenditure is equal to the sum of consumption (C) and investment (I) by firms and government purchases (G). Thus, the planned expenditure (E) can be written as:
E = C + I + G
Using the given consumption function, c = 120 + 0.8 (y - t), where y is the equilibrium income and t is the level of taxes, we can substitute this into the planned expenditure equation. The planned expenditure (E) is then:
E = (120 + 0.8 (y - t)) + 200 + 400
To find the equilibrium income, we set the planned expenditure equal to the national income (y), which gives us the equation:
y = (120 + 0.8 (y - t)) + 200 + 400
By solving this equation for y, we can find the equilibrium income. To calculate the new equilibrium income when government purchases increase to 420, we simply substitute the new value of government purchases (G) into the planned expenditure equation and solve for y. Finally, to calculate the government purchase multiplier, we can use the formula:
Multiplier = ΔY / ΔG
Where ΔY is the change in equilibrium income and ΔG is the change in government purchases.