Question

Problem 3. The Crowding Out Effect. In a closed economy, the consumption function is C = 80+ 0.8YD – 20r, where Yd is disposable income, taxes Tx = 200 and transfers are Tr = 100. The investment function is I = 550 – 130r. Output is Y = 1000. Here the real interest rate is measured in percentage points (e.g. for r = 5% use 5 and not 0.05). (A) Find net taxes T and government spending G if the government budget is balanced. (B) Derive the total savings function S(r). Do savings depend on the interest rate? If yes, positively or negatively? Why could that happen? (C) Find the equilibrium on the loanable funds market: find, at equilibrium, r, S and I. (D) The government raises its spending by 150 and finances this by borrowing. Find the new equilibrium. Does the crowding out effect takes place? If yes, describe it in detail: what crowds out what. If not, explain why. (E) Instead, the government raises its spending by the same 150 and finances this by raising taxes by an equal amount (to keep the budget balanced). Find the new equilibrium. Does the crowding out effect takes place? If yes, describe it in detail: what crowds out what. If not, explain why. (F) Draw the loanable funds market diagram. Show the initial equilibrium and the two equilibria under the two fiscal policies.

Answer 1

Answer :

Given that :

the crowding out effect . in a closed economy , the consumption function is
c= 80+ 0.8yd – 20r,
where  $Y_{D}$ is disposable income , taxes T x=200 and transfers are tr=100.

(A)

Net Tax = T x - TR = 200 - 100 = 100

If budget is balanced,

G = Net tax = 100

(B)

C = 80 + 0.8 x [Y - Net tax - G] - 20 r = 80 + 0.8 x (1,000 - 0) - 20 r = 80 + 800 - 20 r = 880 - 20 r

S(r) = Y - C + (Net tax - G) = 1,000 - 880 + 20 r + 0 = 120 + 20 r

Saving function is positively related to r, because the higher (lower) the r, the higher (lower) the interest income from assets and the more (less) people will save.

(C)

In equilibrium, S(r) = I(r).

120 + 20 r = 550 - 130 r

150 r = 430

r = 2.87

S = 120 + 20 x 2.87 = 120 + 57.4 = 177.4

I = S = 177.4

(D)

New value of G = 100 + 150 = 250

Net tax - New G = 200 - 100 - 250 = - 150

New C = 80 + 0.8 x [Y - Net tax - New G] - 20 r = 80 + 0.8 x (1,000 + 150) - 20 r = 80 + 0.8 x 1,150 - 20 r = 80 + 920 - 20 r

= 1,000 - 20 r

S(r) = Y - C + (Net tax - G) = 1,000 - 1,000 + 20 r - 150 = 20 r - 150

In new equilibrium,

20 r - 150 = 550 - 130 r

150 r = 700

r = 4.67

S = 20 x 4.67 - 150 = 93.4 - 150 = - 56.6 (Indicating dis saving)

I = S = - 56.6

Here, crowding out has taken place. Higher government expenditure has increased borrowing (for deficit financing), increasing interest rate. Higher interest rate has decreased investment, crowing out investment.