4. General Equilibrium An economy consists of two consumers, indexed by j = A, B, who...
a. U(r, 2)xfr + a)°(x2 + b)1-a d. U(,)( h. U(, 2) 1. For each of the utility functions above, find the consumer's opti mal consumption bundle when prices of goods 1 and 2 are pi and P2, and the consumer has an income m 2. For each of the utility functions above, find the consumer's opti mal consumption bundle when prices of goods 1 and 2 are pi and P2, and the consumer has an endowment (e1, e2) of...
Consider an economy with two consumers A and B. Consumers A and B have utility functions u(x+x)= Inx;" + Inx, and (x,x) - Inx' +-Inx, respectively. They face prices P, and P, for good 1 and good 2, respectively, and they have incomes “and I°, respectively a) Write formally the economic problem faced by consumer A and derive the demand functions xi (P1, P2,7") and x(P,P2,7^) [6] b) What are consumer B's demand functions for the two goods 1 and...
Consider an exchange economy with two consumers, A and B, who can consume only two goods. Suppose consumers’ preferences are represented by a Cobb- Douglas utility function of the form u(x1i,x2i) = x1ix2i (here i is for consumer A or B) for a consumption bundle of two goods (x1i,x2i). The consumers have endowments eA = (e1A;e2A) = (4;1) and eB = (e1B;e2B) = (1;4). The price of good 1 is p1 and the price of good 2 is p2. You...
Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 3 units of good X and 5 units of good Y. Consumer B is given an initial endowment of 5 units of good X and 3 units of good Y. Consumer A’s utility function is given by: UA(X,Y) = X + 4Y, and consumer B’s utility function is given by UB(X,Y) = MIN (X, 2Y). If the prices...
3. Consider a two consumer endowment economy. Consumer 1 and consumer 2 come into the economy with an endowment of good x and good y. They can voluntarily trade their endowments. They have the following utility functions and endowments: W:(z,y) = złyt And they have the following endowments: Consumer 1 61 =(4,12) Consumer 2 ez =(8,6) (a) Set up the utility maximization problem for consumer 2. Then solve for the demand functions of good #2 and good y2 as a...
Description of the economy: For each of the following problems, consider a 2x2 Exchange Economy with two consumers A and B, and two goods X and Y . The preferences of consumer A can be represented by the utility function uA(xA, yA) = xAyA , where xA is the amount of good A consumed by consumer A, and yA is the amount of good Y consumed by consumer A. The preferences of consumer B can be represented by the utility...
Description of the economy: For each of the following problems, consider a 2x2 Exchange Economy with two consumers A and B, and two goods X and Y . The preferences of consumer A can be represented by the utility function uA(xA, yA) = xAyA , where xA is the amount of good A consumed by consumer A, and yA is the amount of good Y consumed by consumer A. The preferences of consumer B can be represented by the utility...
Suppose that there two goods X and Y, available in arbitrary non- negative quantities (so the the consumption set is R2). The consumer has preferences over consumption bundles that are strongly monotone, strictly convex, and represented by the following (differentiable) utility function: u(x, y)-y+2aVT, where z is the quantity of good X, and y is the quantity of good Y, and a 20 is a utility parameter The consumer has strictly positive wealth w > 0. The price of good...
3. Consider a two consumer endowment economy. Consumer 1 and consumer 2 come into the economy with an endowment of good x and good y. They can voluntarily trade their endowments. They have the following utility functions and endowments: u1(x,y) = zły: u2(z, 1) = a* * And they have the following endowments: Consumer 1 e1 = (4,12) Consumer 2 e2 = = (8,6) (a) Set up the utility maximization problem for consumer 2. Then solve for the demand functions...
1. Two firms compete in a linear city of length 1 unit. Consumers are uniformly located along the city. Consumer i's utility derived from buying firm j's product is given by jj-(-x)2-Pj where j 1,2 indicate the two firms, t is the per unit cost of travelling along the city, is the location of consumer i, x is the location of firm j, and pj is the price of product j. Product one contains some intrinsically superior features and 22,...