Question

Assume that the consumption function is given by C = 200 + 0, 75(Y − T). Investment is 100; government purchases and taxes are both 100.

(a) This economy has TODAY a GDP of 1700, is this an equilibrium level of GDP? (HINT: Find the AS the AD and compare them).

(b) Will the GDP NEXT WEEK increase or decrease? (HINT: looking to your previous answer see if AS is lower or higher than AD, then think what will happen to production in order to bring the economy back to equilibrium)

(c) What is the equilibrium level of income (GDP)? ii) Describe the process that brings the economy back to equilibrium (using the MAGIC of words)

(d) If government purchases increase to 125, what is the new equilibrium income? (for a fast answer: use the multiplier!). (e) What level of government purchases is needed to achieve an income of 1,600? (again, use the multiplier!)

Answer 1

Consumption(C) = 200 + 0, 75(Y − T)

Investment (I)= 100

Government purchases and taxes are both 100.

G = 100 , T = 100

Aggregate expenditure(AE) = Consumption(C) + Investment (I) +Government purchases(G)

Equilibrium is when income (GDP) (Y) = AE

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a) When GDP is 1700 then Aggregate expenditure = 200 + 0.75(1700 − 100) +100+100 = 200+1200+100+10 = 1600

Aggregate supply (AS) is represented by GDP or Y

Aggregate demand (AD) is represented by Aggregate expenditure (AE)

When GDP(AS) is 1700 then AD is 1600

therefore this is not the equilibrium level of GDP

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b) AS (1700) is less than AD (1600)

So we see that there is excess supply (surplus) of goods,

As a result producers will lowerr there production as a result the GDP will decrease next week

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c)

i) Aggregate level of GDP, Y=AE

Y = 200 + 0.75(Y − 100) + 100 + 100

Y = 400 + 0.75Y − 75

0.25Y = 325

Y = 1300

Equilibrium level of income (GDP) = 1300

ii) At 1700 level of income we saw that supply exceeds demand, as a result producers will cut back production an their inventory investment will fall till equilibrium level of income is achived where income(Y) = AE

or supply is equal to demand

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d) If government purchases increase to 125, what is the new equilibrium income?

Change in G = 25 (125-100)

MPC = 0.75 (slope of the consumption function)

According to multiplier effect:

change in Y/ Change in G = 1/(1-MPC)

Change in Y = 1/(1-0.75)*Change in G

Change in Y = (1/0.25)*25

Change in Y = 100

Therefore new equilibrium level of income = 1300 + 100 = 1400

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e) What level of government purchases is needed to achieve an income of 1,600?

Change in income = 1600 - 1300 = 300

MPC = 0.75

Change in government purchase required = change in Y* (1-MPC)

= 300 (1-0.75)

= 300 *0.25

= 75

Therefore level of government purchases to achieve an income of 1,600 is 175 (100+75)

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