Question

Can you please answer question 2？

1.) Say two customers have identical Cobb-Douglas utilities ua = x.z; and up a's , endowments WA = (2,0) and we = (3,0), and there is a production technology y2 = (41)/3. Person A owns the firm. Find the competitive equilibrium allocation and prices, the equation for the contract curve, and graph these 2.) Now consider the same consumers as problem 1.), but assume instead there is a linear production technology y2 = 2yı owned by person A. Find the competitive equilibrium allocation and prices, the equation for the contract curve, and graph these.

Answer 1

UA= 2 NA NA exility of person A Utility of person B : UB 11 NB XB WA (20) WB = 13,0) 1 Total amount of Good x + x B= 2 +3 - KA + RB 11 Total amount of Good 2 = XA+x*8 Production Technology: Y2 = 24, Calculating marginal utility of Good I marginal utility of Good a MRS (of person A) = MRS: 2 KA MRS (of person B) no κ. B equating MRS (of A) MRS (OB) 2 X 2 XB - XA x B as 2 A 2 20 2 B

have we from Equation KA + x² equation ② from have we 2 2- XA + XB 1 Now, we have ng KA XA & B from equating Mrs. x B.X² XA XB x'o (-x²) = (5-*'B). X² -xo. x B = 58 - x B x 3 2. 5x8 a B Substitute x B=0 in x B. x² Aires we get xo.x²A = 0 (5 - X'A ) . x² 5xA 12 XARA=0

XA X 52h x equilibrium x'A= 5 x B=0 x, B=0, x² = a set of points represe presenting final allocation which are of Pareto efficient. since competitive equilibrium represented bry n'A= 5 equation of contrat ewive. x's Contract cwine is two goods Here, the only x = x² = 0 is the 10 RA "Good 2 98 0 2 Good XA Y ₂ = 2y, Y2 = 2(R'A + x) This decide - 10 I length of 2 Y anis in point E abore competitive equilibrium diagram}