14.02 Quiz 2 Solutions Fall 2004 Multiple-Choice Questions 1) Consider the wage-setting and price-setting equations we studied in class. Suppose the markup, µ, equals 0.25, and F(u,z) = 1-u. What is the natural rate of unemployment in this economy? A) 0.2 B) 0 C) 0.25 D) 0.1 E) 0.5 Answer: A). The wage determination equation is W=Pe F(u,z) or W=Pe(1-u). Since we are in medium-run/long-run equilibrium, P= PeÎ W=P(1-u). The price setting equation is P=W(1+µ). Therefore, W/P=1/(1+0.25)=0.8. From the wage determination equation, we get that W/P=0.8=1-un. Therefore, un = 0.2. 2) In the medium-run/long-run, a decrease in the budget deficit will produce: A) No effect B) An increase in investment C) An increase in consumption D) A decrease in output E) No effect on the price level Answer: B). A decrease in the budget deficit produces a shift of the AD curve to the left. So, in the medium-run/long-run, we will get a decrease in the price level, P, while output will remain unchanged. (Agents are expecting lower prices in the future. Nominal wages fall, and therefore the actual price level decreases. So, the AS curve shifts down, keeping output constant.) From the IS-LM equilibrium, we will have that the interest rate will decrease. Thus, investment will increase, consumption is ambiguous (if the decrease in the budget deficit is achieved using an increase in taxes, consumption will decrease, if not, it will remain constant). Thus, the correct answer is B).3) Suppose that workers in the Republic of Communia are highly unionized, while workers in the Republic of Individuela are not. In all other respects, the two countries are exactly the same. Which statement is true? A) Communia is likely to have a higher natural level of output than Individuela. B) Communia is likely to have a higher natural rate of unemployment than Individuela. C) Wages are probably lower in Communia than in Individuela. D) In the short-run, the price level is always lower in Communia than in Individuela. E) In the short-run, output is always higher in Communia than in Individuela. Answer: B). In our model of the labor market, the level of unionization is captured by the variable z, which affects wages positively (the higher unionization, the more collective bargaining power workers have, which most likely leads to higher wages). Recall that the natural level of unemployment is defined by assuming that P = Pe and by finding the intersection of the wage setting relation W = PeF(u,z) and the price setting relation P = (1+µ)W. Thus, F(un,z) = 1/(1+µ). Higher unionization means that z is higher, which shifts up the wage setting relation and leads to a higher natural rate of unemployment. 4) Suppose the Phillips curve is given by tettu31.0 −+=ππwhere1−=tetθππ Assume that only for the first two periods (t=1 and t=2) people form their expectations using θ=0. From t=3 on, they start using θ=1 forever. Assume that the government still wants to keep unemployment at 2%. What is the expected rate of inflation for t=4? A) 2% B) 4% C) 8% D) 12% E) 16% Answer: C). πt – π t-1 =0.1 – 3(0.02)=0.04 (Inflation goes up every period by 4%.) π 2 =0.04 π3 = 0.08 Î π3 e=0.04 π4 =0.12 Î π4 e=0.08 u W/P Price-setting relation Wage-setting relation 1/(1+µ) un’ un Wage-setting relation’5) You observe that the domestic interest rate increases from 5% to 15%, and you are in a fixed exchange rate system, then this implies that A) The level of the international interest rate increased by 5% B) Agents are expecting a nominal appreciation of 5% C) Agents are expecting a nominal depreciation of 5% D) Both A) and B) E) Both A) and C) Answer: E). Consider the UIP: ttetttEEEii−+=+1*. So if the interest rate increases by 10%, the right-hand side of the equation should also increase by 10%. Thus, A) and C) are not enough by themselves. Option B) produces the opposite effect. Thus, E) is the correct answer.Long Question I (40/100 points) Open Economy IS-LM Assume that the economy is described by the following model: • C = c0 + c1(Y–T), where C is consumption; Y is income; T represents taxes; and c0 and c1 are positive constants • I = b1Y– b2i, where I is investment; i is the interest rate; and b1 and b2 are positive constants • G = __G, where __G is a positive constant • IM = im1Y, where IM is imports; and im1 is a positive constant • X = x1Y* , where X is exports; Y* is foreign income (exogenous); and x1 is a positive constant • The LM equation in this economy is i = 21m (m1Y – Ms), where Ms is money supply (Ms>1); and m1 and m2 are positive constants • Let P*=P=1 Assume that the Marshall-Lerner condition is satisfied (that is, following a depreciation of the exchange rate, the trade balance improves). Note, given that IM = im1Y and X = x1Y* the Marshall-Lerner condition actually does not hold. NX are actually equation to x1Y* -- ε(im1Y), and therefore only the only effect of a depreciation is a price effect. As the currency depreciates, ε increases and NX decrease (not increase!). Whether you used the supposition that the Marshall-Lerner condition holds here or if you used the expressions given to you, we gave you full credit. Part I. Fixed Exchange Rate. Assume for now that the real exchange rate is fixed at one (ε = 1). Assume that the interest rate parity condition holds, and the interest rate in the foreign country is i*. 1. Find the expression for equilibrium income. (2 points) Y = C + I + G + X - εIM = c0 + c1(Y–T) + b1Y – b2i* + __G + x1Y* – (1)( im1Y) Y =11111imbc +−− (c0 – c1T – b2i* + G+ x1Y*) 2. Calculate the change in output (Y), net exports (NX), the domestic interest rate (i), and the real exchange rate if taxes increase by ∆T. Also draw a diagram. (5 points) If there is an increase in taxes, the resulting change in income would be∆Y =11111 imbcc+−−− ∆T (output decreases by11111 imbcc+−− ∆T). NX = X – εIM = x1Y* – im1Y ∆NX = – im1∆Y ∆NX =111111 imbcimc+−− ∆T (net exports increase by111111 imbcimc+−−; the effect on net exports comes through the import side). The domestic interest rate and the real exchange rate do not change, because of the fixed exchange rate regime. So, i=i* and ε=1 (Note that since ε=EP*/P and P=P*=1, ε=E=1.) Money supply must decrease to accommodate the fiscal contraction (monetary policy is endogenous). If it doesn’t, the interest
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