Homework #2 with Answer Key - Analysis of Public Finance | ECON 440, Assignments of Economics

Download Homework #2 with Answer Key - Analysis of Public Finance | ECON 440 and more Assignments Economics in PDF only on Docsity! Econ 440 September 2007 Peter Norman Homework 2 Answer Key 1. 2. a. Max ∏A = (1 – yA – yB)*yA y A FOC: 1 – 2yA - yB = 0 RA (yB) = (1 – yB) / 2 By the same way, RB (yA) = (1 – yA) / 2 By solving reaction functions simultaneously, Nash Equilibrium: yA = 1/3 yB = 1/3 b. ∏C = (1 – 2/3)*(1/3) = 1/9 (same for both firms) c. Max (1 – y)*y y FOC: 1 – 2y = 0 y = 1/2 ( y = yA + yB) yA + yB = 1/2 G = gS + gI = 4 They choose gS and gI in such a way that there will be 4 goats in total. gS = 2 gI = 2 is a possible solution. d. max ∏I = (9 - 2gI – c)*gI gI FOC: 9 - 4gI – c = 0 gI = (9 – c)/4 c = 1 gI = 2 By the same way, gS = 2 Number of goats grazing decreases compared with part b. ∏I * = (9 – 2*2 – 1)*2 = 8 In part b, it was: ∏I = (9 – 8/3 – 8/3 – 1)*8/3 = 64/9 Thus, both of them are better off compared with part b. In part b, there is overproduction. There exists a region on the southwest of the equilibrium where both agents are strictly better off. (2,2) is in this region. 4. max U(x,y) x,y s.t x +py ≤ e max L = U(x,y) – λ (x +py – e) FOC: U1(x,y) – λ = 0 U2(x,y) – λp = 0 U1(x,y) = λ U2(x,y) = λp Solving FOC’s simultaneously, we have; U2(x,y) / U1(x,y) = p a. U(x,y) = x + xy U1(x,y) = 1 + y U2(x,y) = x p = 1 x / (1 + y) = 1 x = 1 + y x + y = 1 (by using constraint of the maximization problem and e = 1) Solving both gives; y = 0 x = 1 welfare measure 1: m* = U(m*, 0) = U(1,0) = 1 value of intervention = m* - e = 1 – 1 = 0 welfare measure 2: x = 1 + y (from FOC) U(e,0) = e = 1 = x + xy x(1+y) = 1 substitute x = 1+y, x2 = 1 x = 1 y = 0 Since x+y = m** m** = 1 value of intervention = e - m** = 1 – 1 = 0 b. U(x,y) = x + y1/2 U1(x,y) = 1 U2(x,y) = (1/2)y -1/2