- Section B Problem 50 Points Answer All Questions Clearly And Succinctly Provide Intermediate Derivations Where Needed 1 (122.26 KiB) Viewed 14 times
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Investment, I, is financed by bank loans and is defined as (2) I=(¹-²), where it is the loan rate, º expected inflation, and I' < 0. Households hold three categories of assets: domestic currency (which bears no interest), deposits with banks, and foreign-currency deposits abroad. All assets are imperfect substitutes. Total household financial wealth FH, is given by: (3) FH = M+D+Ē.D*, where M is currency holdings, and D (respectively D*) domestic (respectively foreign) bank deposits. Financial wealth is predetermined at FH. The demand for deposits is (4) D/M = v(i), where ip is the interest rate on domestic deposits and v' > 0. The foreign-domestic deposit ratio depends on interest rate differential between these assets: (5) E.D*/D = x(iD - iW), where iW is the interest rate on foreign-currency deposits, and x' <0.
Household consumption, C, depends on factor income, interest rates, and wealth: (6) C=C₁Y³ - c₂[(iD - π²) + (iW - πº)] + c3(F¹0/PD), where 0 <c₁ < 1; C2, C3 > 0; and FH is the beginning-of-period stock of household financial wealth. The balance sheet of commercial banks is (7) L=D + LB.
where L = PDI denotes loans to firms, and LB borrowing from the central bank. The interest rate on domestic deposits is (8) iP = iR, where it is the cost of borrowing from the central bank, or the refinance rate. The interest rate on loans is (9) iL = iR +0, where is a risk premium, defined as (10) 0 =0(PPKo - Lo), where Ko is the stock of capital held by firms, Lo beginning-of-period loans, and 0' < 0. The equilibrium condition of the market for domestic goods is (11) (1-x)YS = (1 - 8)C+I+G,
where 0<x< 1 is the fraction of domestic output that is exported (assumed fixed), 0 < 8< 1 is the fixed fraction of total household consumption expenditure allocated to imported goods, and G is government spending. Question B1 [4 points] B1-1. Using equations (9) and (10), write the financial equilibrium condition of the model, in terms of it as a function FF(PD; ¡R, G). [1 pt] B1-2. Explain intuitively the signs of the partial derivatives of the function FF. [3 pts] Question B2 [8 points] B2-1. Using equations (1), (2), (6), (8), and (11), and setting ª = 0, derive the goods market equilibrium condition of the model, in terms of it as a function GG(PD; iR, G). What is the restriction needed on x, 8, and c₁ to ensure that the net supply effect is positive? [5 pts] B2-2. Explain intuitively the signs of the partial derivatives of the function GG. [3 pts] Based on your class notes, represent graphically the equilibrium of the economy in PD-¡L space. Denote the point of equilibrium as point E.
Question B3 [8 points] B3-1. Explain, analytically and graphically, the impact of an increase in government spending, G, when c3 = 0. Is household consumption, C, higher or lower in the new equilibrium, compared to point E? [4 pts] B3-2. Explain, analytically and graphically, the impact of an increase in the refinance rate, iR, when c3 = 0. Is household consumption, C, higher or lower in the new equilibrium, compared to point E? [4 pts] Hint: Differentiate eq. (11) and use the mathematical result dy/dx = (dy/dz)(dz/dx) to calculate dC/dG and dC/diⓇ. The central bank imposes a financial tax on banks, 0 < t < 1, which is passed on fully to borrowers. Thus, the loan rate is now given by, instead of (9), (9') iL=iR + 0 +TL. Question B4 [10 points] B4-1. Using equation (9'), indicate whether an increase in the tax on loans, T¹, affects the equilibrium curves FF and GG. [4 pts] B4-2. Explain movements in curves FF and GG, if any, and describe the transition from the initial equilibrium to the new equilibrium when c3 > 0. [4 pts] B4-3. How does the adjustment process associated with the increase in t differ from what occurs with an increase in the refinance rate, iR? [2 pts]
Suppose now that the economy is at an initial equilibrium Eº, corresponding to the intersection of curves FºFº and GºGº. There is a shock to the economy which leads simultaneously to an autonomous reduction in the premium and an autonomous increase in household consumption. Graphically, curve GG shifts upwards, from GºGº to G¹G¹, whereas curve FF shifts downwards, from F°F to F¹F¹. The new equilibrium is at a point denoted E¹, characterised by higher prices and a lower loan rate. Question B5 [2 points]. Show graphically the equilibrium points Eº and E¹ in PD-i¹ space. Suppose that the policy authorities would like to return the economy to the original equilibrium point, Eº, by using monetary and fiscal policies.
Question B6 [18 points] B6-1. Using the diagram built to answer question B5 as a starting point, study if a reduction or an increase in government spending, G, can bring the economy from point E¹ back to point Eº. Either way, explain why. [4 pts] B6-2. Using the diagram built to answer question B5 as a starting point, study if a reduction or an increase in the refinance rate, iR, can bring the economy from point E¹ back to point Eº. Either way, explain why. [4 pts] B6-3. Using the diagram built to answer question B5 as a starting point, study if the combination of an increase in the refinance rate, iR, and either an increase or a decrease in government spending, G, can bring the economy from point E¹ back to point Eº. Either way, explain why, and identify the key parameter which determines whether G should be increased or reduced. [9 pts] B6-4. What is the fundamental reason why monetary policy by itself, or fiscal policy by itself, may or may not be able to bring the economy from point E¹ back to point Eº? [1 pt] NOTE: In answering B6-1 to B6-3, use different colors to illustrate the shifts, if any, in FF and GG associated with the policy change(s) under consideration.