Consider a 2x2 pure exchange Edgeworth box economy model where each individual has preferences given by...

Consider a 2x2 pure exchange Edgeworth box economy model where each individual has preferences given by U(x, y) = sqrt(xy)

Consumer A is endowed with 1 unit of x and 2 units of y. Consumer B is endowed with 3 units of x and 1 unit of y. What is the ratio of the price of prices, Px/Py, that will clear both markets when the consumers individually solve the UMP?

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Rahul Sunny answered 2 years ago

Consider a 2x2 pure exchange Edgeworth box economy. Consumer A’s preferences are given by Ua(x, y)...

Consider a 2x2 pure exchange Edgeworth box economy. Consumer A’s preferences are given by Ua(x, y) = min(x, y) Consumer B’s preferences are given by Ub(x, y) = y + x Both consumers are endowed with 1 unit of x and 2 units of y. Which of the following identifies the set of Pareto efficient allocations that are feasible given the dimensions of the Edgeworth box? Yb = Xb The set of points where Ya = Xa as well as...

Consider a 2x2 pure exchange Edgeworth box economy. Each consumer is endowed with two units of...

Consider a 2x2 pure exchange Edgeworth box economy. Each consumer is endowed with two units of x and one unit of y. Consumer A has (strictly) monotonic preferences over good x and is otherwise indifferent between any levels of good y. The preferences for consumer B are given by Ub(x, y) = x + 2y. What ratio of prices Px/Py will clear both markets?

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For 2x2 pure exchange economies, assume both preferences are homothetic, also assume smooth and quasiconcave utility...

For 2x2 pure exchange economies, assume both preferences are homothetic, also assume smooth and quasiconcave utility functions (so preferences are convex). Assume also that the locus of efficient allocations is a continuous curve connecting the two endpoints of the main diagonal in the Edgeworth box. Show that all efficient allocations lie on the same side of the main diagonal in the Edgeworth box. What if both preferences are identical? Thank you!

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Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences...

Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences that can be represented by the following utility function: u(X1, X2) = X1 + X 0.5 2 Let P1 = 4 and P2 = 2. In addition, suppose this individual has an income of $120. (a) Write down the expression for this consumer’s marginal rate of substitution of X1 for X2 (MRS12). Identify the distinguishing feature of this particular MRS12. (b) Calculate the optimal...

Consider a pure exchange economy with 2 goods and 3 agents. Goody is the numeraire,...

Consider a pure exchange economy with 2 goods and 3 agents. Good y is the numeraire, so we set py = 1. • Mr. 1 is Cobb-Douglas of type λ = 0.25 and is endowed with (10, 4). • Mr. 2 is Cobb-Douglas of type λ = 0.5 and is endowed with (5, 9). • Mr. 3 is Cobb-Douglas of type λ = 0.75 and is endowed with (20, 20). In the following steps, you will find the equilibrium of...

Consider a pure exchange economy with two consumers, Ann (A) and Bob (B), and two commodities,...

Consider a pure exchange economy with two consumers, Ann (A) and Bob (B), and two commodities, 1 and 2, denoted by (x^A_1, x^A_2) and (x^B_1, x^B_2). Ann’s initial endowment consists of 5 units of good 1 and 10 units of good 2. Bob’s initial endowment consists of 10 unit of good 1 and 5 units of good 2. The consumers’ preferences are represented by the following utility functions:U^A(x^A_1, x^A_2) =min{x^A_1, x^A_2} and U^A(x^B_1, x^B_2)= =min{x^B_1, x^B_2}. Denote by p1 and...

Consider a pure exchange economy with two consumers, Ann (A) and Bob (B), and two commodities,...

Consider a pure exchange economy with two consumers, Ann (A) and Bob (B), and two commodities, 1 and 2, denoted by (x^A_1 , x^A_2 ) and (x^B_1 , x^B_2 ). Ann’s initial endowment consists of 15 units of good 1 and 5 units of good 2. Bob’s initial endowment consists of 5 unit of good 1 and 5 units of good 2. The consumers’ preferences are represented by the following Cobb-Douglas utility functions: U^A(x^A_1 , x^A_2 ) = (x^A_1 )^2...

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Consider a pure exchange economy with 2 goods and 3 agents. Good y is the numeraire, so we set py = 1. • Mr. 1 is Cobb-Douglas of type λ = 0.25 and is endowed with (10, 4). • Mr. 2 is Cobb-Douglas of type λ = 0.5 and is endowed with (5, 9). • Mr. 3 is Cobb-Douglas of type λ = 0.75 and is endowed with (20, 20). In the following steps, you will find the equilibrium of...

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Consider a 2x2 pure exchange Edgeworth box economy model where each individual has preferences given by...

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