a) Show the equilibrium points E0 and E1 in a PD-z diagram. Using this diagram, study if an increase or a reduction in government spending can bring the economy from E1 back to E0. Either way, explain why. b) Using this diagram, study if an increase or a reduction in the refinance rate, iR, can bring the economy from E1 back to E0. Either way, explain why. c) Using this diagram, study which combination of a change in the refinance rate, iR and in government spending, G, can bring the economy from E1 back to E0. Either way, explain why.
Consider a small open economy producing a good which is an imperfect substitute for a foreign good. There are five categories of agents: firms, households, commercial banks, the central bank, and the government. The world price of the foreign good is taken as exogenous and normalized to unity. The nominal exchange rate, E, is flexible.
The supply of the domestic good is given by
- YS * =YS * (PD) *
Where PD is the price of the domestic good and YS = d YS’ /d PD > 0
Investment, I, is financed by bank loans and is defined as
- 1 = I(iL)
Where iL is the loan rate and I’ < 0
Households hold three categories of assets: cash (which bears no interest), deposits with domestic banks, and foreign-currency deposits abroad. Assets are imperfect substitutes. Household financial wealth, F ^ H is defined as:
- FH = M+D+E.D*
Where M is cash holdings, and D (respectively, D*) domestic (respectively, foreign) deposits.
The demand for deposits is
- M / D = m,
Where ID is the interest rate on domestic deposits, and m > 0 is a constant coefficient.
The demand for foreign deposits depends on the domestic and foreign interest rates:
- E0D* /F0H =h ( ID ,i* ),
Where F0H is the predetermined component of household financial wealth, E0 ISthe nominal exchange rate at the beginning of the period, iD the interest rate on domestic deposits, i* the interest rate on foreign deposits, and h0 is a share function with partial derivatives
∂h/∂iD<hiD <0, ∂h/∂i* = hi*>0.
Household consumption spending, C, depends on factor income, interest rates, and wealth:
- C = c1 YS -c2 (iD +i^*) + c3(F0H / PD)
where 0< c1< 1, c2, c3 >0.
The balance sheet of commercial banks is
- L = D + LB
Where L = PDI denotes loans to firms, and LB borrowing from the central bank
The interest rate on domestic deposits is
- ID = IR
Where IR is the cost of borrowing from the central bank, or the refinance rate.
The interest rate on loans is
- IL = IR + Ꝋ
Where Ꝋ is a premium, defined as
- Ꝋ = Ꝋ (PD * K0 – L0)
Where L0 is beginning-of-period loans and Ꝋ ≤ 0
The equilibrium condition of the market for domestic goods is
- YS – X(z) = (1 – delta)C + 1 + G,
Where G is government spending, X exports, z = E / (PD) the real exchange rate (defined such that an increase is a
The equilibrium condition of the market for foreign exchange is given by
Z-1 * [X(z) – delta*C] +(1+i*) D0* -(D* -D0* ) = 0.
Suppose that the foreign interest rate, i*, rises.
Let E1 denote the new equilibrium point, corresponding to the intersection of the new
Question
a) Show the equilibrium points E0 and E1 in a PD-z diagram.
Using this diagram, study if an increase or a reduction in government spending
can bring the economy from E1 back to E0. Either way, explain why.
b) Using this diagram, study if an increase or a reduction in the refinance rate, iR, can bring the economy from E1 back to E0. Either way, explain why.
c) Using this diagram, study which combination of a change in the refinance rate, iR and in government spending, G, can bring the economy from E1 back to E0. Either way, explain why.
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