Question

In: Economics

1.) Individual A and B have the following preferences: uA = (x1A) · (x2A)3 and uB...

1.) Individual A and B have the following preferences: uA = (x1A) · (x2A)3 and uB = (x1B ) · (x2B ). Their endowments are given by ωA = (3, 0) and ωB = (0, 3). Solve for (and graph) competitive equilibrium and the contract curve.

2.) Individual A and B have the following preferences: uA = ln(x1A) + ln(x2A) and uB = ln(x1B ) + ln(x2B ). Their endowments are given by ωA = (2, 6) and ωB = (2, 4). Solve for (and graph) competitive equilibrium and the contract curve.

3.) Now re-solve problem 2 but replace individual A’s preferences with uA = x1Ax2A +x2B. That is, individual B has a positive externality on individual A.

Solutions

Expert Solution

Rahul Sunny answered 7 months ago
Next > < Previous

Related Solutions

Person A and B both have Cobb-Douglas preferences, uA = (x1A)2/5 · (x2A)3/5 and uB =...
Person A and B both have Cobb-Douglas preferences, uA = (x1A)2/5 · (x2A)3/5 and uB = x1B · x2B . Their endowments are wA = (0, 2) and wB = (4, 0). Find their demand functions and use market clearing to derive equilibrium price for good two, p2 (set p1=1, and enter your answer as a simplified decimal).
Consider the following social welfare function: SW=Ua(Xnca, Xca, Xc~a, Pa)+Ub(Xncb, Xcb, Xc~b, Pb)+ Ud(Xncd, Xcd, Xc~d,...
Consider the following social welfare function: SW=Ua(Xnca, Xca, Xc~a, Pa)+Ub(Xncb, Xcb, Xc~b, Pb)+ Ud(Xncd, Xcd, Xc~d, Pd)+... where: X=consumption bundle, P=pollution, nc=non-competitive consumption, c=competitive consumption, a, b, d = people, ~a, ~b, ~d = all other people besides a, b, d. 1. Place positive and negative signs above all the terms in the function, illustrating whether they increase or decrease each individual’s utility.
Consider the following social welfare function: SW=Ua(Xnca, Xca, Xc~a, Pa)+Ub(Xncb, Xcb, Xc~b, Pb)+ Ud(Xncd, Xcd, Xc~d,...
Consider the following social welfare function: SW=Ua(Xnca, Xca, Xc~a, Pa)+Ub(Xncb, Xcb, Xc~b, Pb)+ Ud(Xncd, Xcd, Xc~d, Pd)+... where: X=consumption bundle, P=pollution, nc=non-competitive consumption, c=competitive consumption, a, b, d = people, ~a, ~b, ~d = all other people besides a, b, d. Let Xcb be a new house overlooking a canyon. Let P be the reduction in scenic beauty experienced by the community. Finally, let Xc~b be the status impact on folks who are not b arising from the new McMansion....
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 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...
You cross the following two individuals: Individual 1: A/a;B/b;C1/C2 Individual 2: a/a;B/b;C1/C2 A is fully dominant,...
You cross the following two individuals: Individual 1: A/a;B/b;C1/C2 Individual 2: a/a;B/b;C1/C2 A is fully dominant, B is dominant lethal, whereas C1 and C2 are incompletely dominant The proportion of offspring that are expected to have the same phenotype as individual 1 is _________
1. Consider the preferences of an individual over two goods, x and y, with prices px...
1. Consider the preferences of an individual over two goods, x and y, with prices px and py and income I. (a) If the individual's preferences can be represented by the utility function u(x,y) =2x1/2 + y, what is the marginal rate of substitution? What does this MRS imply about how this consumer would trade y for x? Are the underlying preferences homothetic (explain)? Graphically illustrate a typical indifference curve and explain how you know the shape. (b) If the...
Consider 3 individuals A, B & C with the following risk profiles (4 points) Individual A:...
Consider 3 individuals A, B & C with the following risk profiles (4 points) Individual A: P(healthy) = 90% and I(healthy) = 1000 and I(sick) = 0 Individual B: P(healthy) = 95% and I(healthy) = 3000 and I(sick) = 500 Individual C: P(healthy) = 99% and I(healthy) = 4000 and I(sick) = 500 P() = probability I() = Income An insurance company has agreed to cover these individuals for $1000 each. They have to pay a premium of 100. True...
2. The utility function for Abe (A) and Bro (B) are as follow: UA = XAYA...
2. The utility function for Abe (A) and Bro (B) are as follow: UA = XAYA UB = XBYB0.5 Where the initial endowment of X and Y are: XA = 20, YA = 20, XB = 8, YB = 100 a) Calculate the marginal rate of substitution of X and Y for Abe and Bro at their initial endowment point. b) Assume that the amount of X and Y is fixed, draw the Edgeworth diagram and label the initial allocation...
1. Explain how diversity of individual preferences based on variations in individuals’ marginal rates of substitution...
1. Explain how diversity of individual preferences based on variations in individuals’ marginal rates of substitution gives rise to voluntary exchange and mutual gains from trade. 2.   Discuss the variety of ways in which technological change may affect the relative productivity of capital and labor, the capital or labor intensity of production methods and resulting relative shares of total output distributed to workers and capital owners.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT