An economy has the follwoing comsumption function: C= 200+ 0.8di
The government budget is balanced with government purchases and taxes both fixed at $100. Net exports are $100. Investments $600. Find the equilibrium GDP.
What is the multiplier for this economy? If G rises by $100 what happens to Y? What happens to Y if both G and T rise by $100 at the same time?
Take a shot, what do you think:
Hints:
Y=C+I+G+(X-M),
S+T=I+G and since T=G, S=I. So first calculate S (Savings)
Hint2: whatever you don't consume out of disposible income (di) is savings, so S= -200 + .2di
ten
How to find the multiplier? I've got the equilibrium GDP, but I can't find anything about the multiplier.
To find the equilibrium GDP in this economy, we need to set the total spending in the economy equal to the GDP. The components of spending are consumption (C), government purchases (G), investments (I), and net exports (NX). The equation for total spending is:
Y = C + G + I + NX
Given the consumption function C = 200 + 0.8DI, where DI represents disposable income, we can substitute this into the equation for total spending:
Y = (200 + 0.8DI) + G + 600 + 100
Since the government purchases (G) and net exports (NX) are fixed at $100 each, we can simplify the equation:
Y = 200 + 0.8DI + 800
Now, to find the equilibrium GDP, we need to determine the value of disposable income (DI) that satisfies the equation. Since the government budget is balanced, taxes (T) should be equal to government purchases (G), which is $100. Therefore, DI = Y - T, and substituting in our equation:
Y = 200 + 0.8(Y - T) + 800
Since T = G = $100, we rewrite the equation:
Y = 200 + 0.8(Y - 100) + 800
Expanding and simplifying:
Y = 200 + 0.8Y - 80 + 800
Combine like terms:
Y = 920 + 0.8Y
Subtracting 0.8Y from both sides:
Y - 0.8Y = 920
0.2Y = 920
Dividing by 0.2:
Y = 4600
Hence, the equilibrium GDP in this economy is $4600.
To find the multiplier for this economy, we can use the formula for in any given economy:
Multiplier = 1 / (1 - Marginal Propensity to Consume)
Since the marginal propensity to consume (MPC) can be found from the consumption function (C = 200 + 0.8DI), which is the coefficient of DI, the MPC in this case is 0.8. Therefore, the multiplier would be:
Multiplier = 1 / (1 - 0.8) = 1 / 0.2 = 5
So, the multiplier for this economy is 5.
If government purchases (G) rise by $100, the effect on the equilibrium GDP (Y) can be calculated by using the multiplier. Since the multiplier is 5, the change in GDP (ΔY) would be:
ΔY = Multiplier * ΔG = 5 * $100 = $500
Therefore, the GDP (Y) would rise by $500 if government purchases increase by $100.
If both government purchases (G) and taxes (T) rise by $100 at the same time, the effect on the equilibrium GDP (Y) would depend on the marginal propensity to consume (MPC) and the multiplier. However, since taxes (T) and government purchases (G) are balanced in this scenario (T = G), the change in GDP (ΔY) would be minimal. The increase in taxes (T) would offset the increase in government purchases (G), resulting in a negligible change in GDP (Y).