Section B Problem (50 points) Answer all questions clearly and succinctly. Provide intermediate derivations where needed

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Section B Problem 50 Points Answer All Questions Clearly And Succinctly Provide Intermediate Derivations Where Needed 1 (155.68 KiB) Viewed 12 times

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 (composite) 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 = Nº(K), where N is employment, Ko is the stock of capital at the beginning of the period and 0<a,ß<1. The price of the domestic good is PD, and the nominal wage is fixed at W. CONTINUED OVER 3 of 5 Question B1 14 points]. Solve for labor demand. Nº, and the supply of goods, Y', which maximize profits. What is the restriction needed, if any, on a and B to ensure a positive relationship between output and the domestic price? Write the equation for the supply of goods, Y, as equation (2). Investment, I, is financed by bank loans and is defined as (3) 1=1(¹), where it is the loan rate 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 F", is given by: (4) F" M+D+E.D", tivaly D*) domestic (respectively foreign) bank
(4) FH = M+D+ED*, where M is currency holdings, and D (respectively D*) domestic (respectively foreign) bank deposits. Financial wealth is predetermined at F". The demand for deposits is (5) D/M = v(i), where i is the interest rate on domestic deposits and v'>0. The foreign-domestic deposit ratio depends on the interest rate differential between these assets: ED*/D-x(iP-iw), where iW is the interest rate on foreign deposits, and x' <0. Household consumption, C, depends on factor income, the domestic interest rate, and wealth: (7) C=C₁Y' - c₂iD + c3(F¹/PD), CONTINUED OVER 4 of 5 where 0 <c₁ <1; C2, C3 > 0; and F" is the beginning-of-period stock of household wealth. 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) iP=iR, where it is the cost of borrowing from the central bank, or the refinance rate.
tent.blackboardcdn.com/5f0eeec577cec/21719653?X-Blackboard-Exp CD Page view A Read aloud TAdd text (9) P=1R, where it is the cost of borrowing from the central bank, or the refinance rate. The interest rate on loans is (10) i=i+0. where 0 is a risk premium, defined as (11) 0 0(PDKo-Lo), where Ko is the stock of capital held by firms and Lo is beginning-of-period loans, and 0 <0. Question B2 [2 points]. Explain the rationale underlying equations (10) and (11). The equilibrium condition of the market for domestic goods is (12) Y-X=(1-8)C+1, where X represent exports, assumed exogenous, and 08 <1 is the fixed fraction of total consumption which spent on imported goods. Question B3 16 points] B3-1. Using equations (10) and (11), derive the financial equilibrium condition of the model, in terms of it as a function FF(PD; iR). [3 pts] B3-2. Explain intuitively the signs of the partial derivatives of the function FF 13 ptx| CONTINUED OVER 5 of 5 Question B4 [10 points] B4-1. Using equations (2), (3), (7), (9), and (12), derive the goods market equilibrium condition of the model, in terms of it as a function GG(PD; iR). [4 pts] B4-2. Explain intuitively the signs of the partial derivatives of the function GG. 14 pts] B4-3. Represent graphically the equilibrium of the economy in PD-j¹ space and state (without proof) the condition on the relative slopes of the equilibrium curves. [2 pts]