Question

Let: C = consumption, Ip = investment spending (as a function of price level), G = government spending, Tx = tax revenue, Yd = after-tax income, Assume for a given closed economy:

C=100 + 0.9 Yd – 20P

Ip= 400 – 40P G=300

T=100

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

P=1.41 + 0.0001Y

a. According to the investment equation (Ip= 400 – 40P) as overall price level in the economy increases investment spending decreases. How could you explain this situation? Please use graphs to elaborate your answer.

b. Find the equilibrium level of overall price and aggregate output in this economy. What would be the value of consumption and investment spending at this equilibrium?

c. How 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?

d. Compare equilibrium values of investment spending and consumption you find in parts (c) and (d). How would you explain the changes? Elaborate your answer for both investment and consumption.

Answer 1

a) I = 400 - 40P

If there is rise in price level, people will spend more money on consumable goods and will left with less money to save. Less saving will reduce the overall investment level.

b) 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 = 800 + 0.9Y - 90 - 60P

Y = 710 + 0.9Y - 60P

0.1Y = 710 - 60P

where P = 1.41 + 0.0001Y

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

0.1Y = 710 - 84.6 - 0.006Y

0.106Y = 625.4

Y = 5,900

P at this Y would be: 1.41 + 0.0001 * 5,900 = 2

Consumption = 100 + 0.9 * (Y - 100) - 20P = 100 + 0.9 * (5,900 - 100) - 20 * 2 = 5,280

Investment = 400 - 40 * 2 = 320

c) If new government spending = 400

Y = C + I + G

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

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

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

Y = 900 + 0.9Y - 90 - 60P

Y = 810 + 0.9Y - 60P

0.1Y = 810 - 60P

where P = 1.41 + 0.0001Y

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

0.1Y = 810 - 84.6 - 0.006Y

0.106Y = 725.4

Y = 6,843.39

P at this Y would be: 1.41 + 0.0001 * 6,843.39 = 2.09

Consumption = 100 + 0.9 * (Y - 100) - 20P = 100 + 0.9 * (6,843.39 - 100) - 20 * 2.09 = 6,127.25

Investment = 400 - 40 * 2.09 = 316.4

d) When government spending rises, consumption rises and investment level falls. Rise in government spending will raise rate of interest because it will shift the IS curve to its right which will lower the investment level in part (c) than in part (b). Consumption will rise because some part of government spending will be attributed to transfer payments and subsidies.