Consider the following exchange economy: u (x1, x2) = min{2x1, x2} u³ B (x, x) = min{x, 2x} =(2, 2) B = (2, 2) Let P₁/p2 denote the relative price. Suppose = 1. (a) Show that both markets clear at this relative price by computing the optimal consumption plan for each consumer and showing that these plans are feasible.
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- 3 Consider a pure exchange economy with 2 consumers and 2 goods. Consumer ? owns 8 units of good 1 and 1 unit of good 2, and his preference is represented by the following utility function: uA(x1, x2) = x1*x2. Consumer ? owns 2 units of good 1 and 4 units of good 2, and his preference is represented by the following utility function: uB(x1,x2)=x1+x2. Assume that the two consumers are allowed and able to trade with each other, and that good 1 is the numeraire. In this case, both consumers act as price-takers. Price takers: a market participant that is not able to dictate the prices in a market. Therefore, a price taker must accept the prevailing market price. Please find the competitive equilibrium of this pure exchange economy.6Please no written by hand
- Set up a utlitiy maximization problem given the following information.Give typing answer with explanation and conclusion Consider an exchange economy consisting of two people, A and B, endowed with two goods, 1 and 2. Person A is initially endowed with ωA = (0,10) and person B is initially endowed with ωB = (11,0). They have identical preferences, which are given by U^A(x1,x2) = U^B(x1,x2) = x1^2*x2. Suppose that p2 =1. Under the competitive equilibrium, what is p1? Round answers to two decimal places.6. (b) Consider an exchange economy with two agents Á and B, and two goods i and y. Consumption of the two goods is given by: U^(XA,Ya) = XÂYA U^(xa,Y^) = xfy1-a) U®(Xg,Ys) = ×BYS „(1-b) Where x, is agent A's consumption of good x etc. Let the agents' initial endowments be: Good Agent A 1 B 1 (%)- i) Find competitive equilibrium price ratio */P. ) for this economy. ii) Why is it sufficient to compute the market clearing price ratio for just one market (say) to answer (i).
- Solve it correctly please. I will rate accordingly.Consider a pure exchange economy with two goods and two agents, A and B. Agents A and B have the same utility u (1, y) = /TY. Since the agents' initial allocations are given by eA = (4.2) and eB = (2.4), then the Walrasian equilibrium will be composed of the following consumption baskets: %3D O (XA,YA )=(2,2) e (Xg,Ye) = (4,4) (Xa, YA)=(1,0) e (Xg,Yg)=(5,6) (XA,YA)=(2,4) e (Xg,YB)=(4,2) (XA,YA)=(3,3) e (Xg,Ye)=(3,3) o (XA,YA)=(1,1) e (Xg,YB)=(5,5)please only do: if you can teach explain steps of how to solve each part of formula ? x(p,w)={(2w/3p1,w/3p1) if p1<p2(2w/3p1,w/3p2) if p1≥p2 ? how to solve for this