Assume an open, mixed economy. That is, foreign trade is part of the economy, an

Question

Assume an open, mixed economy. That is, foreign trade is part of the economy, and the economy includes both a public (government) and a private (consumers and businesses) sector. Given this, aggregate demand is expressed as (C + I + G + X). Assume the MPC is .7. Assume a stimulus package of $100 billion has been approved by Congress and the money has been spent. In order to pay for those expenditures, Congress also approved a $100 billion increase in individual income taxes. Will these actions by Congress expand or contract the economy or are they just useless actions? Get started early and work with your class members to solve this problem.

Explanation / Answer

Y = C+I+G+X

C= a+b(Y-Tax)

Tax = To+t*Y (autonomous tax, and t is tax rate)

putting C and T in y equation

Y = a+b(Y-To-tY)+I+G+X

taking y term on one side

Y(1+bt-b) = a - bTo +I+G+X

Y (1-b + tb) = a-bTo+I+G+X

Coefficient of To= -b/(1-b+tb)

coefficient of G = 1/(1-b+tb)

coefficient of To is less than coefficient og Go as 0<b<1, so the impact of government expenditure is higher than increase in tax rate. so overall the impact of srategy will increase in short run output increment.

dY = (-b*dTo + dG)/(1-b+tb) > 0

t = zero

dY = (dG - b*dTo)/(1-b) = (100-.7*100)/.3 = 30/.3 = 100

so income will increase by 100 billion dllars.

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