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
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
- 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
- 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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