ECON20032
Macroeconomics 4
Semester 2, 2023-24
Practice Exam
Section A
Questions (10 points each; total: 30 points)
Answer succinctly (in no more than 120 words each) all of the following three
questions. All answers must be written in complete sentences. Do a word count and indicate the number of words after each answer.
Question A1. As a share or GDP, private investment and private savings are, respectively, 10.4 and 8.3 percent in country A, and 12.7 and 11.5 percent in country B. Also as a share of GDP, public investment and public savings are, respectively, 3.4 and 3.8 percent in country A, and 2.7 and 1.5 percent in country B. What is the current account deficit of each country? Does either one exhibit evidence of twin deficits?
Question A2. Describe the main features of the global foreign exchange market.
Question A3. What are financial frictions and how do they affect the loan rate? Provide an example.
Section B
Problem (50 points)
Answer all questions clearly and succinctly. Provide intermediate derivations where needed, but do not exceed 8 pages, graphs included, in your answers.
Consider a small open economy producing a single good, which is an imperfect substitute for a foreign good. There are four categories of agents: firms, households, commercial banks, and the central bank (CB). The world price of the foreign good is taken as exogenous and normalized to unity. The nominal exchange rate is fixed at E(-) .
Output, Y, is produced by combining labour and capital:
(1) Y = Na(K0)β,
where N is employment, K0 is the stock of capital at the beginning of the period, and 0 < a,β < 1.
The price of the domestic good is PD, and the nominal wage is fixed at W(-) .
Question B1 [4 points]. Solve for the profit-maximizing level of labor demand, Nd, and the supply of goods, Ys. What is the restriction needed, if any, on C and β to ensure a positive relationship between output and the domestic price?
Write the equation for the supply of goods, Ys, as equation (2).
Investment, I, is financed by bank loans and is defined as
(3) I = I(iL),
where iL is the loan rate and I′ < 0.
Households hold three categories of assets: domestic currency (which bears no interest), deposits with banks at home, and foreign-currency deposits abroad. All assets are imperfect substitutes. Total household financial wealth FH, is given by:
(4) FH = M + D + E(-) .D*,
where M is currency holdings, and D (respectively D*) domestic (respectively foreign) bank deposits. Financial wealth is predetermined at FH0 .
The demand for domestic deposits depends on the interest rate differential:
(5) D/FH0 = d(iD - i*),
where iD (i*) is the interest rate on domestic (foreign) deposits and d′ > 0.
Similarly, the demand for foreign deposits is
(6) E(-) .D*/FH0 = d*(iD - i*),
where d* ′ < 0.
Question B2 [4 points]. Derive the share of cash, m(), from equations (4), (5), and (6). Indicate the restrictions needed to ensure that a) m is positive; and b) an increase in the domestic deposit rate lowers the share of cash in financial wealth.
Household consumption, C, depends on income from production and the domestic interest rate:
(7) C = c1Ys - c2iD,
where 0 < c1 < 1 and c2 > 0.
The balance sheet of commercial banks is
(8) L = D + LB,
where L = PDI denotes loans to firms, and LB borrowing from the central bank.
The interest rate on domestic deposits is
(9) iD = iR,
where iR is the cost of borrowing from the central bank, or the refinance rate.
The interest rate on loans is
(10) iL = iR + θ,
where θ is a default premium, defined as
(11) θ = θ[(PDK0 - L0)/L0],
where L0 is loans to firms at the beginning of the period, and θ′ < 0.
Question B3 [2 points]. Explain the rationale underlying equations (10) and (11).
The equilibrium condition of the market for domestic goods is
(12) Ys - X(-) = (1 - δ)C + I,
where X(-) represent exports, assumed exogenous, and 0 < δ < 1 is the fixed fraction of total consumption which is spent on imported goods.
Question B4 [6 points]
B4-1. Using equations (10) and (11), derive the financial equilibrium condition of the model, in terms of iL as a function FF(PD; iR). [3 pts]
B4-2. Explain intuitively the signs of the partial derivatives of the function FF. [3 pts]
Question B5 [10 points]
B5-1. Using equations (2), (3), (7), (9), and (12), derive the goods market equilibrium condition of the model, in terms of iL as a function GG(PD; iR). [4 pts]
B5-2. Explain intuitively the signs of the partial derivatives of the function GG. [4 pts]
B5-3. Represent graphically the equilibrium of the economy in PD-iL space and state (without proof) the condition on the relative slopes of the equilibrium curves. [2 pts]
Question B6 [14 points]
B6-1. Examine, analytically and graphically, the impact of an increase in the refinance rate, iR. [6 pts]
B6-2. Explain graphically how the financial accelerator effect operates. [4 pts]
B6-3. Examine, analytically and graphically, in a separate diagram, what happens when θ ′ = 0 in equation (11). [4 pts]
The central bank requires now banks to hold a fraction 0 < μ < 1 of the deposits that they
receive from households as reserves. As a result, the deposit rate is now given by, instead of (9),
(9′) iD = (1 - μ)iR.
Question B7 [10 points]
B7-1. Using equation (9’), and in the general case where c2 > 0 in equation (7), show how an increase in μ, the required reserve ratio, affects the equilibrium curves FF and GG. [4 pts]
B7-2. Explain movements in curves FF and GG, if any, and describe the transition from the initial equilibrium to the new equilibrium. [4 pts]
B7-3. How is the transition affected when c2 = 0? Does consumption increase or fallin that case? [2 pts]