The utility possibility frontier is defined as the set of maximum utility levels for all consumers that is feasible in the economy, given resource constraints and preferences. For a two-consumer economy, it is defined formally as the solution to: u₁₁ (ūB) = max uд(xA) subject to иB(xB) ≥ йB and (XA, XB) feasible. For each of the economies above, find an equation for the utility possibilities frontier, and graph it.

Two friends, Minrui and Jing, share a flat and both consume internet (i) and all other goods (g). The utility function for Minrui is U_m=i^(0.3)g^(0.7) whereas the utility function for Jing is U_m=i^(0.1)g^(0.9). Considering that the income of both individuals are the same $500 and that the prices are p_i = $80 and p_g = $5, what would be the optimal allocation of public good (i) and private good (g)? Interpret your answer.

Nora's utility function is given by U = In(C) + In(L), where U is utility, C is consumption, and L is leisure. The total time Nora has is T = 1 and is a utility maximizer. Before the Covic pandemic, the wage rate is 10, and Nora has no non-labor income. When the pandemic hit and part of the economy was locked down, Nora's wage rate decreased to 8. However, the government provided income support by sending out a non-labor income of 5 to everyone, including Nora. Nora still has a total amount of time T = 1 for leisure and work during the pandemic. Which of the following statements is correct? O Before the pandemic, Nora's labor supply is 0.2. O Before the pandemic, Nora spent time equal to 0.2 O Before the pandemic, Nora's consumption was 9. O During the pandemic, Nora's labor supply is 0.5. leisure. O During the pandemic, Nora was better off for having a higher utility level. O During the pandemic, Nora's labor supply is unchanged becauses income effects were perfectly offset by the…

Starting with utility function U= U(X, Y) and budget constraint PxX+ PyY= M, derive the equili- brium condition using calculus.

An individual's utility function is given by: U (q1 , q2) = q11/2 . q2 Suppose we know that the individual is maximizing their utility by consuming 9 units of good #1 (q1=9) and six units of good #2 (q2=6). If the current price for good #1 is $1 (p1=1), what must be the price of good #2 (p2) and what must be the individual's current income (y) available to spend on the two goods? a.) p2 = b.) y=

= 5. Consider an economy with a single (representative) agent with utility function u(x, lc) = x¹/514/5 and an endowment of 0 units of x and 10 units of time, which the agent can use as leisure (c) or labor (L) (i.e., L + lc = 10). The agent owns a firm that produces good x using L as an input, with technology of production given by x(L) = 3√L. Let the price of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage). Find the competitive price of time w and the competitive allocation.

Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y   Which of the following is NOT true about Reese’s preference? (a) The MRS decreases when x increases.(b) The preferences are homothetic.(c) The marginal utility of y is higher when x = 10 than when x = 5.(d) For any a > 0, Reese prefers the bundle (x =a/2 , y = a/2 ) over either the bundle (x = a, y = 0) or (x = 0, y = a).

Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. The consumers have the following utility functions: UA(X1A,X2A)=X1A+3X2A; UB(X1B,X2B)=X1B +X2B. Consumer A is initially endowed with 4 units of good A and no unit of good 2, that is, consumer A's initial endowment is (w1A,W2A)=(4,0). Consumer B is initially endowed with 3 units of good 2 and no unit of good 1, that is, (w1B,W2B)=(0,3). In order to implement the allocation (x1A,X2A)=(0,1), (x1B,X2B)=(4,2) as a Walrasian equilibrium, what transfer of wealth should we make between the consumers if good 1 is the numeraire, that is, if p1 =1? An amount 7 of wealth should be transferred from consumer A to consumer B. O a. O b. None of the other answers. O c. An amount 3 of wealth should be transferred from consumer A to consumer B. O d. An amount 3 of wealth should be transferred from consumer B to consumer A. e. An amount 7 of wealth should be transferred from consumer B to…

For a consumer with a utility function u=3x^2y^2 when px=3 and py=4, find the consumption levels that maximize his utility under the $120 budget constraint. What is the maximum benefit?

Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…