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) Ip = 400 - 40P

If there is rise in price level, people will spend more money on consumable goods which will leave people 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 ............... (1)

where Aggregate Supply: P = 1.41 + 0.0001Y .............. (2)

0.1Y = 710 - 60 * (1.41 + 0.0001Y), by putting value of P from (2) in equation (1)

0.1Y = 710 - 84.6 - 0.006Y

0.106Y = 625.4

Y = 5,900

Thus, equilibrium level of Income is 5,900

P at this Y would be: 1.41 + 0.0001 * 5,900 = 2 (by putiing value of Y in (2)

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

Investment = 400 - 40 * 2 = 320 (by putting value of P in investment function)

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) If government spending rises, aggregate output will rise. 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) because rate of interest and investment level have negative relationship with each other. Rise in consumption is associate with spending by government on transfer payments, subsidies etc.