# intermediate Macroeconomics

homework3 (1).pdf1Assume that we can model output demand using:Y =1 1−(1−s)[G−(1−s)T + C0 + I(r)]where I(r) = Ω−ωr Additonally assume that the Government has a balanced primary budget:∆T = ∆GIn the short run in the following settings compare the value of ∆Y ∆G. Is it larger than 0? Is it smaller or larger than 1?1. Suppose the economy has a central bank that ﬁxes the interest rate at rc2. Suppose there is no speculative demand for money, ie Quantity Theory holds. That is M P V = Y3. Suppose have standard money demand equation :M PV [r + πe]γ = Y2Suppose a country has a positive debt to nominal gdp ratio ( b > 0) that isn’t increasing overtime. This implies that the primary deﬁcit to nominal gdp ratio satisﬁes : −d r−gy = b1additionally assume r > gY . There is news that the population growth rate in the country is expected to become negative. Given this news, how does gY change? (Hint: in standard solow model what is the steady state growth rate of (non-per capita) gdp, Y?) Given this is the debt to nominal gdp ratio growing or falling after the news? If this causes the risk premia to change, what happens to r ? What does this do to the growth of the debt to nominal gdp ratio?3Under Full Ricardian Equivalence in the short run. Does a decrease in taxes : • increase investment? • increase private savings (Y -T – C) ? • cause Y to increase?4What is the condition on the primary deﬁcit to nominal gdp ratio in order for country to be solvent ( that is, ∆b ≤ 0) when taking seignorage into account?5In the short run , accounting for the marginal propensity to invest η , is it possible that government spending in a closed economy can ﬁnance itself? What if η = 0 ? Is it possible for goverment spending to pay for itself in the short run in a fully open economy?6Suppose that the exchange rate from e is 10euro dollar . In addition assume the nominal exchange rate in the US is 10% . If the nominal interest rate in Germany is 7% and the exchange rate next period will be 1:1, where would you invest? For which exchange rate next period would you be indiﬀerent about where to invest?7 Compare the Eﬀects of Fiscal Stimulus (G ↑) in ﬂexible and ﬁxed exchange rate fully open economies in both the short and medium run. What happens toY,M P,Nx,e,tt28In the fully open economy what happens toY,Nx,e,Af;t+1in the short run if inﬂation expectations fall?9If a country has persistant trade deﬁcits ( Nx < 0) what is happening to the capital account? What eﬀects could this have on interest rates?10Compare the eﬀects of an increase in exporter sentiment, Xs in the partially open economy model with a central bank. First, assume the central bank is ﬁxing an interest rate r = rc. How does r,e,Y,Nx,M P change in the short run? Compare this to the results if instead of ﬁxing an interest rate, the central bank ﬁxes an exchange rate in the fully open case.11Assume consumers live for two periods. Each consumer has an income of 10 in each period. Finally assume that the real interest rate, r = 1/2. Let Consumer A be a keynesian consumer with s = 1/2 and autonomous con- sumption C0 = 5 Let Consumer B, follow the pernament income hypothesis and attempts to smooth consumption so that they are as similar as possible in both periods (re- call from lecture that this means ρ = r, also pernament income here is simply Y1 + Y2 1+r ) (Hint : use the following to solve for Consumer B’s consumption: 1) C2 C1 = (1+r) 1+ρ 2) C1 + C2 (1+r) = Y1 + Y2 (1+r) ) Compare the changes to consumption in period one and two in the following scenarios:1. Income doubles today.2. Income doubles tomorrow.3. Income today increase by 5 and decreases next period by 7.54. The interest rate falls to 1/4 , assume ρ = 1/2 still. repeat 1,2,3 when Consumer B can’t borrow so that C1 ≤ Y1.