Question 4: Suppose we have two people in the market: A, B. Their utility functions are UA = min{ X1, X2), UB = min{x1, 2}. Solve their optimal choices and then find market demand.

Suppose we have two people in the market: A, B. Their utility functions are UA min{x1, x₂}, UB = min{x₁,2}. Solve their optimal choices and then find market demand. =

Suppose there are 2 individuals, A and B; 2 goods, X and Y. The utility function of A: U, = X, + YA and the utility function of B: Uz = X3 + Y3. YB- Draw the pareto set in an Edgeworth Box.

Suppose that there are two goods (X and Y ). The price of X is $2 per unit, and the price of Y is $1 per unit. There are two consumers (A and B). The utility functions for the consumers are UA (X, Y): = X0.5y-0.5 UB (X,Y)= X0.8y-0.2 Consumer A has an income of $100, and Consumer B has an income of $300. PAGE 2 (a) Use Lagrangians to solve the constrained utility-maximization problems for Consumer A and Consumer B. (b) Calculate the marginal rate of substitution for each consumer at his or her optimal consumption bundles. (c) Suppose that there is another consumer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's marginal rate of substitution at her optimal consumption bundle? Why?

uestion1:Donna and Jim are two consumers purchasing strawberries and chocolates. Jim’s utility function is U (x, y) = xy and Donna’s utility function is U (x, y) = x2y where x denotes strawberries and y denoteschocolates. Jim’s marginal utility functions are MUX=y and MUy=x while Donna’s are MUX=2xy and MUy=x2. Jim’s income is $100, and Donna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4? What is the optimal bundle for Jim, and for Donna, when the price of strawberries rises to $3?Question2:Consider a one-period eco

For the utility function U = Qx0.15Qy(1-0.15) find the trade-off rate between good X and good Y at Qx= 9 and Qy=13

Pedro, a retired economics professor, grows lemons and oranges in his back- yard. He consumes some of these fruits, and sells some in a local farmer's market. Pedro's preferences are represented by the following utility function U(x, y) = min{x,y}. In one season he can harvest 20 pounds of lemons and 60 pounds of oranges. In the local market, price of lemons is $4 per pounds and price of oranges is $2 per pound. Pedro receives $300 income from his retirement plan per season. Question 1 Part a Find Pedro's optimal consumption bundle. Make sure to draw his budget con- straint and indifference curves to show his optimal choice. Question 1 Part b Suppose that the price of lemons rises to $5 per pound. What is Pedro's optimal consumption bundle now? Decompose the total change in demand due to a price change into a substitution effect, ordinary income effect and endowment income effect and graphically demonstrate it.

Julio loves gardening. His favourite plants are tulips and hydrangeas. His utility function is ' u(t,h)= t +100h -h^2 where t is the number of tulipsin his garden and h is the number of hydrangeas in his garden. suppose he has a 500 square feet for his garden. each tulip takes up 1 square foot of space and each hydrangeas takes up 4 square feet. he gets both plants for free.If he wanted to maximize his utility, how many tulips should he plant, what about hydrangeas? b) if his yard was only 144 square feet, how many tulips would he plant? How many hydrangeas? C) In order to plant both tulips and hydrangeas, how big does his garden need to be. carfeully explain.

Given a Utility function: U(x,y) = 3xy. Suppose the Price of x is 2, and the price of y is 4. What is the optimal choice of y as a function of x. ( MRS = (Px/Py).

Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, when there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is ua(XA,S)=XA.S, where xĄ is the amount of money Person A owns. Person B's utility function is ug(xg, 1s)=xB .(1-s), where xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Person A has the legal right to a fill up the room with smoke and there exists a market for smoke "abatements". At the Walrasian equilibrium, how much money will person B be left with? O a. Xg=1.25 O b. Xp=2.25 O c. XB=0.25 O d. Xg=0.25 е. None of the other answers.