Economics 442: Macroeconomic Policy - Problem Set 1

Q1. Suppose the economy is described by the following equations (so we are looking at a closed economy):

-Real Sector

(1) Y = Z                          Output equals aggregate demand, an equilibrium condition

(2) Z = C + I + G             Definition of aggregate demand

(3)  C = c_o + c₁Y_D           Consumption fn, c₁ is the marginal propensity to consume

(4) Y_D ≡ Y - T + T_r           Definition of disposable income

(5) T = t₁Y                      Tax function; 1t is marginal tax rate.

(6) T_r = TR₀                    Transfer payments; TR0 is lump sum transfers.

(7) I = b₀ - b₂i                Investment function

(8) G = GO₀                    Government spending on goods and services, exogenous

-Asset Sector

(9) M^d/P = M^s/P               Equilibrium condition

(10) M^s/P = M₀/P              Real money supply

(11) M^d/P = μ₀ + Y - hi     Real money demand

1. Solve for the IS curve (Y as a function of i).

2. Solve for the LM curve (i as a function of Y). What is the channel by which monetary influences affect the real goods sector in this model?

3. Solve for the equilibrium value of Y.

4. Graph the IS and LM curves on one diagram. Clearly indicate the intercepts and the slopes. Label the equilibrium income and interest rate Y₀ and i₀.

Q2. Assume G increases by ΔGO, and is completely bond financed (and there are no portfolio effects here).

1. Calculate the government spending multiplier.

2. Suppose instead T_r decreases by ΔTR. Calculate the government transfers multiplier.

3. Redraw your answer to 1.4. Then in the same graph, show what happens to the equilibrium income and interest rate if government spending on goods and services is increased by ΔGO. Include in your graph the level of income that would be achieved if somehow the interest rate stayed constant (label this point Y_A).

4. At the new equilibrium, do we know if investment is higher or lower than the level it started out at? Do we know if it is higher or lower than at Y_A?

5. Suppose the Fed targets the interest rate at i0 (call this i_target). Returning to 2.3, show graphically what happens if government is increased. What happens to the level of investment?

Q3. Consider a situation where the economy is in a liquidity trap.

1. Draw a diagram illustrating the situation where interest rates are at the zero lower bound.

2. Show what happens to the equilibrium income and interest rate if the money supply is increased.

3. Show what happens if lump sum taxes are increased. Does investment rise or fall? (Recall: lump sum taxes are like the inverse of transfers).

4. Suppose investment behaves as in the textbook: I = b₀ + b₁Y - b₂i

Does investment rise or fall?