Question

Consider a two-period lived representative agent for an economy, whose preferences for consumption are described by the lifetime utility function U = InC1 + InC2 a. Compare the effects of a temporary and a permanent income fall on current account. Suppose that the output of the economy in the two periods are 100 (Y1) and 100 (Y2), and r is 5%. b. Does the economy run a trade balance deficit or surplus in period 1? How about period 2? Explain your answer with a graph. c. How would answer to part b change if Y1 and Y2 are 150 and 50 respectively? Explain your answer with a graph.

Answer 1

solution:

U = Inc,t in Ca Y = 50 Y2 = 200 8 = 5% = 0.05 (a) optimal choice MRS= MRE Juldi - (Ho) Joldcz citoi) 2 = 1.05 CU - (2= 1.050 Buchet constraint ºn teams of Future Valuee Cat C (1+r) = M2 + milito) => 1.0501 + ci(1+0.5)= 200 + 50 (1+0.05) = 1.05ct 1.050 - 200 + 50+ 2.5 =) 2010 - 252.5 qe = 120.2380 whereas current out fut is 50 so Cormorant Trade dejicit in year-I = 120.238. - 50

120.2380 - 50 - 70.2380 =(70.2380 $ (Consumption-output) = 7062380 if b= 1$) C₂ = 1.0501 = C2 = 1.05 (120.2380). = 126.2499 Toode Balonce surfius in year-2. Susplus - 7 - C2 - 200- 12.6.2499 = 73.7501 = (73.7501 $ if bel & 2 • Surplus • 200-126.24 Vit 12 (1+z)=260 1 = 73.7501 1 Y2 = 2004 son 126.25=24 - te TIC -Cl y = 50 G YIT Y2 - 24004762 1 120.2380 (1+r) G- Y1 = 70.2380 (dejicit

m2 = 12 (b) When Y2 = 30 C2 = 1.0501 me=VI 77 Cat CCitr) = mz+micito) 1.050, + 1.0561= 30+50 (1.05) 2.100 = 30 + 52.5 = Ci = 8205 201 =) ( = 39.2857 in Period- I Toode Balance Sus pues Because Y, SC Suropius = Y,-a = 50-39.2857 = 10.71423 = 10.71423 $ if b= 1$. So Ca= 1.0501 = 1.05 (39.2857) = 41.249985 There Jore Trade Balance Deficit in year-2 Because Y₂ LC2 and deficit = C2-Y2 = 41.249985-30 - 11.2499 = 11.2499$ if þ=1$

m2 = 12 (b) When Y2 = 30 C2 = 1.0501 me=VI 77 Cat CCitr) = mz+micito) 1.050, + 1.0561= 30+50 (1.05) 2.100 = 30 + 52.5 = Ci = 8205 201 =) ( = 39.2857 in Period- I Toode Balance Sus pues Because Y, SC Suropius = Y,-a = 50-39.2857 = 10.71423 = 10.71423 $ if b= 1$. So Ca= 1.0501 = 1.05 (39.2857) = 41.249985 There Jore Trade Balance Deficit in year-2 Because Y₂ LC2 and deficit = C2-Y2 = 41.249985-30 - 11.2499 = 11.2499$ if þ=1$

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