Question

In: Economics

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?

  1. Yb = Xb

  2. The set of points where Ya = Xa as well as the points on the edge of the box where Xa = 2 and Ya > 2

  3. Ya = Xa

  4. The set of points where Yb = Xb as well as the points on the edge of the box where Xb = 2 and Yb > 2

Solutions

Expert Solution


Related Solutions

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?
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?
In a two-person, two commodity, pure exchange economy Person A’s utility is given by UA (q1A,...
In a two-person, two commodity, pure exchange economy Person A’s utility is given by UA (q1A, q2A) = q1A * q2A + 2q1A + 5q2A and Person B’s utility is given by UB (q1B, q2B) = q1B * q2B + 4q1B + 2q2B. Where commodity one is w1 and commodity two is w2, if Person A has wA = (w1A, w2A) = (78,0) and Person B has wB = (w1B, w2B) = (0,164), what is the uncompensated demand function for...
3. Consider a pure exchange economy with two goods, wine (x) and cheese (y) and two...
3. Consider a pure exchange economy with two goods, wine (x) and cheese (y) and two con- sumers, A and B. Let cheese be the numeraire good with price of $1. Consumer A’s utility function is UA(x,y) = xy and B’s utility function is UB(x,y) = min[x,y]. A has an initial allocation of 10 x and no y, and B has an initial allocation of 10 units of y and no x. (a) Put wine x on the horizontal axis...
Consider a consumer with preferences over two goods (good x and good y) given by u...
Consider a consumer with preferences over two goods (good x and good y) given by u ( x , y ) = x ⋅ y. Given income of I and price of good yas $ P yper pound and price of good xgiven as $ P xper pound, the consumer chooses the optimal consumption bundle given as x ∗ = I 2 P x and y ∗ = I 2 P y . Given P x = $ 1per pound...
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!
Consider a pure exchange economy with 2 goods and 3 agents. Good y 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 2x2 exchange economy where the two individuals A and B engaged in the exchange...
Consider a 2x2 exchange economy where the two individuals A and B engaged in the exchange of the two goods x and y have utility functions U A = x A − y A − 1 and U B = y B − x B − 1, respectively. The individuals' endowments are { ( w A x , w A y ) , ( w B x , w B y ) } = { ( 5 , 10 )...
Suppose a consumer has preferences given by U(X,Y) = MIN[2X,Y]. Suppose PX = 1 and PY...
Suppose a consumer has preferences given by U(X,Y) = MIN[2X,Y]. Suppose PX = 1 and PY = 2. Draw the Income Consumption Curve for this consumer for income values • M = 100 • M = 200 • M = 300 To do this, carefully draw the budget constraints associated with each of the prices for good X, and indicate the bundle that the consumer chooses in each case. Also, be sure to label your graph accurately.
6. Consider a pure exchange economy with two individuals, Sarah and James, and two goods, X...
6. Consider a pure exchange economy with two individuals, Sarah and James, and two goods, X and Y . For Sarah, goods X and Y are perfect complements (Leontief preferences), so her utility function is US = min {XS, YS}. For James, goods X and Y are perfect substitutes, so his utility function is UJ = XJ + YJ . Suppose the economy has 100 units of good X and 50 of good Y . Draw indifference curves for Sarah...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT