Public Affairs 974 Fall 2012 - 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; t₁ is marginal tax rate.

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

(7) I = b₀ + b₁Y - 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

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

1.2 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?

1.3 Solve for the equilibrium value of Y.

1.4 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 (no portfolio effects here).

2.1 Calculate the government spending multiplier.

2.2 Suppose instead Tr increases by ΔTR. Calculate the government transfers multiplier.

2.3 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).

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

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

Q3. Consider the Aggregate Demand-Aggregate Supply framework. Suppose investment spending decreases when we are not in a liquidity trap (and do not end up in a liquidity trap), and the Fed does NOT target the interest rate. You can assume for simplicity expected inflation is always zero.

3.1 Show what happens in an IS-LM and AD-AS graph in the period the investment spending reduction occurs.

3.2 Show what happens over time to output, the price level, and the interest rate.

3.3 Show what the IS-LM and AD-AS graphs look like if initially, the economy is not in a liquidity trap, but interest rates are very close to zero, and output is below potential GDP/full employment. Then show what happens if potential GDP shifts out a lot because entrepreneurs develop new products due to tax rate reductions and deregulation.

Q4. 4.1. Look up on Bloomberg or elsewhere the yield on a one year T-bill. Calculate the price as if the bond were to mature one year from now (specify the date you looked up the data). Show your calculations.

4.2 Once again, look up the one year and two year yields. Assuming the expectations hypothesis of the term structure holds, what is the expected interest one year interest rate, one year from today. Show your calculations.

4.3 Draw the yield curve, for 3 months to 30 years.

4.4 Assuming the expectations hypothesis of the term structure holds (i.e., there is no liquidity premium), do you expect the US economy to go into recession in the next year? Why or why not?

Q5. Compute the price of a share of stock that pays a $1 per year dividend and that you expect to be able to sell in one year for $20, assuming you require a 15% return.

Q6. 6.1 Calculate the price of a share of stock, assuming dividends are expected to be constant at D₀ = 1 and (rf + rp) is also expected to be constant at 0.05. Show your algebraic work.

6.2 Suppose that you revise your expectations regarding (rf + rp) downward by 2 percentage points. What immediately happens to the price of the share of stock? Once again, show your work.