3. Suppose that the behavior of households and firms in an economy is determined

Question

3. Suppose that the behavior of households and firms in an economy is determined by the following equations $C=20+0.8Yd, II = 40, G = 30, T = 0.2Y Transfers are equal to zero. Taxes are proportional to income. a. Calculate an expression for aggregate demand as a function of income. b. Calculate the equilibrium level of output. c. Calculate the level of taxes at the equilibrium level of output. d. Is the government running a budget surplus or a budget deficit at the equilibrium level of output? What is its size? e. Assume that government spending increases to G' = 80 (G = 50). What is the new equilibrium level of output? 3. Suppose that the behavior of households and firms in an economy is determined by the following equations $C=20+0.8Yd, II = 40, G = 30, T = 0.2Y Transfers are equal to zero. Taxes are proportional to income. a. Calculate an expression for aggregate demand as a function of income. b. Calculate the equilibrium level of output. c. Calculate the level of taxes at the equilibrium level of output. d. Is the government running a budget surplus or a budget deficit at the equilibrium level of output? What is its size? e. Assume that government spending increases to G' = 80 (G = 50). What is the new equilibrium level of output? 3. Suppose that the behavior of households and firms in an economy is determined by the following equations $C=20+0.8Yd, II = 40, G = 30, T = 0.2Y Transfers are equal to zero. Taxes are proportional to income. a. Calculate an expression for aggregate demand as a function of income. b. Calculate the equilibrium level of output. c. Calculate the level of taxes at the equilibrium level of output. d. Is the government running a budget surplus or a budget deficit at the equilibrium level of output? What is its size? e. Assume that government spending increases to G' = 80 (G = 50). What is the new equilibrium level of output?

Explanation / Answer

a)

C = 20 + .8Yd

I = 40

G = 30

T = 0.2Y  

Equation of aggregate demand is given by Y = C+ I +G  

Y = 20 + .8Yd + 40 + 30

= 90 + .8(Y-T)

= 90 +.8(Y - .2Y)

= 90 + .8(.8Y)

= 90 +.64Y is the required equation of aggregate demand

b)

at equlibrium

Y = 90 + .64Y

Y - .64Y = 90

.36Y = 90

Y = 90/.36

Y = 250

so equlibrium output is 250

c) we have G = 30

T = 0.2Y

= .2(250)

= 50 is the level of taxes at equlibrium

d)

So BS = T - G  

T- G = 50 - 30

government is running with budget surplus of $20

e)

G' = 80 or

G = 50

at equilibrium

Y = C + I +G'

= 20 + .8Yd + 40 + 80

= 140 + .8(Y - T )

= 140 + .8(Y - .2Y)

= 140+ .8(.8)

= 140 + .64Y

Y - .64Y = 140

.36Y = 140

Y = 140/.36

= 388.88 is new equilibrium level of output

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