Models and Solutions

Question 1

relationship between nominal and real interest rate

Answer 1

1+r_t+1 = (P_t/P_t+1)(1+R_t+1) = (1 + R_t+1 )/ (1+π_t+1)

Question 2

phillips curve for unemployment/ inflation

Answer 2

u^t= u* + k(π_t^e-π_t)

Question 3

budget constrain of household in small, open economy

Answer 3

P_tC_t^D+S_tP_t*C_t^M+P_tI_t+B_t+1+S_tB_t+1*=P_tF(K_t)+(1+R_t)B_t+(1+R_t*)S_tB*_t

Where S_t is the exchange rate

Question 4

small, open economy assumption assumes that _______ are endogenous and _______ are exogenous

Answer 4

foreign prices are interest rates are exogenous;

domestic prices and interest rates are endogenous.

We are solving for the domestic prices and interest rates, taking the foreign ones as given.

Question 5

FOC in a small, open economy model

Answer 5

C_t^D ; C_t^M ; K_t+1 ; B_t+1 ; B*_t+1

You need to solve with respect to foreign and domestic consumption goods, household investment, amount of nominal bonds bought in dollars, and nominal bonds bought in foreign currency

tldr; foreign/domestic goods/bonds, investment

Question 6

Law of One Price

aka

Purchasing Power Parity Condition

Answer 6

if there are no trade costs, then the price of foreign and domestic goods when denominated in the same currency are the same

P_t=S_tP*_t

this is derived from the first two FOC (with respect to foreign and domestic consumption goods)

Question 7

small, open economy - conditions needed for euler equation

Answer 7

FOC with respect to C_t^D, C^D_t+1, and Kt+1

C_t =C_t^D+C_t^M

Then, once you have two non-arbitrage conditions, plug those in

Question 8

no-arbitrage condition between investing in capital and in domestic goods in a small, open economy

Answer 8

FOC of K_t+1, B_t+1

Question 9

no arbitrage condition for investment in domestic and foreign bonds

Answer 9

FOC of B_t+1, B​*_t+1

and the fact that S_t=P_t/P_t+1

Question 10

The Uncovered Interest Rate Parity

Answer 10

no-arbitrage condition between investment in foreign and domestic goods

Question 11

economy-wide resource constraint in a small, open economy

Answer 11

household production = domestic goods consumed plus investment plus exports:

F(K_t)=C_t+I_t+X_t-C^M_t

Question 12

Money in Utility Model FOC (3 agents)

Answer 12

HH: consumption, labor, capital, real bonds, real money demand

C_t, L_t, b_t+1, m_t+1, K_t+1

Firm: capital, labor

K_t, L_t

Government: don’t need FOC! just plug solutions from firm and HH into budget constraint

Question 13

equations and unknowns in Money in the Utility function model

Answer 13

r_ss, w_ss, r^k _ss, L_ss, C_ss, K_ss

SO wages and rental rates of labor are NOT given, but they are determined along with labor, consumption, and capital by plugging the FOCs of the firm and the household into the government BC