Question

Consumption: ?? = 4 + 0.5(? − ?) Investment: ?? = 4 + 0.2? Government expenditure: ? = 30 Tax revenue: T = 0.2? Exports: ? = 7 Imports: ? = 0.02 ? where Cd is consumption on domestically produced goods (remember: total consumption, C=Cd +M), Y is domestic output, G is government expenditure, M is imports, IP is planned investment spending, X is exports, and T is tax revenue.

(i) Derive the equation for planned aggregate expenditure (PAE) on domestically produced goods as a linear function of domestic output, Y.

(ii) Find the short-run equilibrium value for output, Y, for this economy.

(iii) What is the multiplier’s value for a unit increase in exports?

(iv) Illustrate the equilibrium on a 45-degree diagram.

(v) Calculate the government budget deficit (G-T) (vi) Calculate the equilibrium value of net exports (NX=X-M).

(vii) Suppose there is an increase in exports, X from 7 to 8. a. Calculate the effect on short-run equilibrium output. By how much does it increase? b. Illustrate your answer on the diagram. c. Calculate the change in eq

Answer 1

Planned aggregate expenditure is aggregate consumption plus planned investment spending.

PAE = C + Ip

PAE = Cd + M + Ip

PAE = 4 + 0.5(? − ?) + 0.02 ? + 4 + 0.2?   

PAE = 4 + 0.5(? − 0.2?) + 0.02 ? + 4 + 0.2?

PAE = 8 + 0.22 ? +0.5(0.8?)

PAE = 8 + 0.22 ? +0.4?

PAE = 8 + 0.42 ?

Y = C + I + G + (X-M)

Y = 4 + 0.5(? − ?) + 4 + 0.2? + 30 + ( 7 - 0.02 ? )

Y = 4 + 0.5(? − 0.2?) + 4 + 0.2? + 30 + ( 7 - 0.02 ? )

Y = 45 + 0.2? + 0.5(0.8?) - 0.02 ?

Y = 45 + 0.2? + 0.4? - 0.02 ?

Y = 45 + 0.58 Y

Y - 0.58 Y = 45

0.42Y = 45

Y = 45/0.42

Y = 107.14

(iii) Multiplier value of export = 1/ 1 - mpc + mpm

mpc = 0.5 and mpm = 0.02

Value of marginal propensity to consume is derived from ?? = 4 + 0.5(? − ?). In this equation mpc is 0.5, and value of marginal propensity to import is dericed from the equation for import ( ? = 0.02 ?) .

Multiplier value of export = 1/ 1 - mpc + mpm = 1/0.52 = 1.92

(iv) The place where AS = AD is the equilibrium. The equilibrium income is 107.14

AS = CAS+G+ NX AD=C+I+G+ NX Consumption (Investment 107.14 Income

(v) Government budget deficit (G-T)= 30 - 0.2? = 30 - 0.2 * 107.14 = 30 - 21.428 = 8.572

(vi) NX= X - M = 7 - 0.02 ? = 7 - (0.02 * 107.14) = 7 - 2.1428 = 4.8572

Y = C + I + G + (X-M)

Y = 4 + 0.5(? − ?) + 4 + 0.2? + 30 + ( 8 - 0.02 ? )

Y = 4 + 0.5(? − 0.2?) + 4 + 0.2? + 30 + ( 8 - 0.02 ? )

Y = 46 + 0.2? + 0.5(0.8?) - 0.02 ?

Y = 46 + 0.2? + 0.4? - 0.02 ?

Y = 46 + 0.58 Y

Y - 0.58 Y = 46

0.42Y = 45

Y = 46/0.42

Y = 109.52

The output increases by 109.52 - 107.14 = 2.38

b.

AS = C+S + G + NX AD = 46+0.58 AD=C+I+G+ NX = 45+0.58Y Consumption (Investment 107.14 109.52 Income