Question

C=consumption, Ip=investment spending (as a function of price level), G=government

spending, Tx=tax revenue, Yd=after-tax income, a given closed economy:

C=100+0.9Yd–20P

Ip=400–40P

G=300

T=100

Moreover, the aggregate supply curve for this economy is defined by the following equation:

P=1.41+0.0001Y

1Find the equilibrium level of the overall price and aggregate output in this

economy. What would be the value of consumption and investment spending at this

equilibrium?

2How would the equilibrium aggregate output and price level change if

government spending increases to Gnew=400? What would be the value of consumption

and investment spending at this new equilibrium?

3Compare equilibrium values of investment spending and consumption you find

in parts(2)and(1). How would you explain the changes? Elaborate your answer for both

investment and consumption.

Answer 1

1. Equilibrium level of the overall price and aggregate output

Y = C + I + G

C = 100 + 0.9(Y - T) - 20P

Y = 100 + 0.9( Y -T) -20P + 400 - 40P + 300

Y = 100 + 0.9( Y - 100) - 20P + 400 - 40P + 300

Y = 100 + 0.9Y - 90 - 20P + 400 - 40P + 300

Put like terms together

Y - 0.9Y = 100 + 400 + 300 - 90 - 20P - 40P

0.1Y = 710 - 60P

Where P = 1.41 + 0.0001Y

Therefore;

0.1Y = 710 - 60( 1.41 + 0.0001Y)

0.1Y = 710 - 84.6 - 0.006Y

Put like terms together

0.1Y + 0.006Y = 625.4

0.106Y/0.106 = 625.4/0.106

Y = 5,900

At equilibrium level

The value of consumption will be

P at Y will therefore be;

1.41 + 0.0001Y

Where Y = 5,900

Therefore;

1.41 + 0.0001( 5,900)

= 2

Therefore consumption will be;

Consumption = 100 + 0.9( Y - 100) - 20P

= 100 + 0.9( 5,900 - 100) - 20( 2)

= 100 + 5,220 - 40

= 5,280

Investment will also be;

Ip = 400 - 40P

Where P = 2

Therefore;

I = 400 - 40(20

= 400 - 80

= 320

2.New government spending = 400

Gnew = 400

Y = C + I + G

Where C = 100 + 0.9( Y - T) - 20P

Y = 100 + 0.9( Y - 100) - 20P + 400 - 40P + 400

Y = 100 + 0.9Y - 90 - 20P + 400 - 40P + 400

Put like terms together

Y - 0.9Y = 810 - 60P

0.1Y = 810 - 60P

Where P = 1.41 + 0.0001Y

Therefore;

0.1Y = 810 - 60( 1.41 + 0.0001Y)

0.1Y = 810 - 84.6 - 0.006Y

Put like terms together

0.1Y + 0.006Y = 725.4

0.106Y/0.106 = 725.4/0.106

Y = 6,843.40

Therefore;

P at Y will be

=1.41 + 0.0001( 6,843.40)

=1.41 + 0.68434

=2.094

Consumption will be;

Consumption= 100 + 0.9( Y -100) - 20P

= 100 + 0.9( 6,843.40 - 100) - 20( 2.094)

= 100 + 6,159.06 - 90 - 41.88

= 6,127.18

Investment = 400 - 40P

Where P = 2.094

= 400 - 40(2.094)

= 316.24

3.

a)Government spending is directly and indirectly proportional to consumption and investment respectively. This is evident that when the government spending increases, also consumption increases but on the other hand investment level decreases. Increase in government spending triggers the rate of interest to increase because it will lead to the shifting of the IS curve to the right thus lowering the level of investments in part 2 than in part 1. Consumption will automatically increase because part of the government spending will go to funding of the payment transfers and as well as subsidies.