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: U3 = X3 + YB. Draw the pareto set in an Edgeworth Box.
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- Which of the following statements captures the meaning of transitivity of preferences?a. If A is preferred to B, then B is less preferred than A.b. If A is preferred to B, and B is preferred to C, then A is preferred to C.c. If A is preferred to B and B is preferred to C, then the preference for A over B is stronger than the preferencefor B over C.d. If A is preferred to C, then there exists B such that A is preferred to B and C is preferred to A.Ralph and Graham have identical utility functions, U (x, y) = x² + y². There are 10 units of x and 10 units of y to be divided between them. a. What are the fair allocations in this case?Consider two consumers, A and B, who consume two goods, x and y. Assume that the utility function for A is UA Ay and the utility function for B is UB = BYB. Consumer A is endowed with 10 units of x an 10 units of y. Consumer B is endowed with 10 units of x and 40 units of y. Consider consumer A alone, what share of their income do they spend on each good? Share on x Share on y = [Choose ] 1/2 2/3 1/4 3/4 ✓ 1 1/3
- Please Show ALL Workings VERY CLEARLY! marginal utilityI. You only consume two goods and your preferences are represented by utility function U(x₁, x₂) = (x0.5 + x2.5)² for x₁ > 2 and x₂ > 0. 1. Find your marginal utility for each good. Simplify your answers. Based on your answers, are your preferences strictly monotonic? Why or why not? 2. Do your preferences obey the law of diminishing marginal utility for each good? Why or why not? If not, what is the behavior of your marginal utility for each good? Use calculus and words to answer this question.For each of the following utility functions, compute the marginal utility of good X (MUx) and the marginal utility of good Y (MUY). a. U(X,Y) = 3X1/2 + 5Y1/2 b. U(X,Y) = X0.5y0.4
- compute the marginal utility of good X (MUX) and the marginal utility of good Y (MUY).a. U=U ( X ,Y )=3 X1 /2+5Y1/ 2For problems 1, 2, 3, we consider an agent Ann who consumes goods and y and has a utility U (x, y) = x²y. In these problems, Good costs P and good y costs Py. (1) Ann has I to spend. (a) Write out Ann's utility maximization problem. (b) Find: MU, MUy, and MRSxy. (c) Write out Ann's tangency condition. What is the other equation needed to solve for Ann's demand? (d) Find Ann's demands for x and y as functions of Pr, Py, and I. (Partial credit if you do this only for I = 30, P₂ = 5 and Py = 2.)10. Consumer A and B have each been given an allocation of 2 goods x and y (assume each has positive amounts of both goods). At this allocation, consumer A has an MRS of 2, while consumer B has an MRS of 1/2. Could this allocation be Pareto efficient? Explain why or why not.
- What is the marginal utility per dollar spent on the 6th strawberry? Which of the combinations of strawberries and apples satisfies the following rule? How do you know?Remy and Emile consume only cheese (x,) and strawberries (x2). Remy's preferences are described by UR = min{xf, 2x5}while Emile's preferences are described by UE = xf + x5 . Remy has 8 pieces of cheese and 1 pint of strawberries while Emile has 4 pieces of cheese and 3 pints of strawberries. (a) Draw an Edgeworth box with x, on the horizontal axis and x, on the vertical axis. Position Remy on the bottom left corner and Emile on the top right corner. Indicate the total number of units of x, and x2. Label the endowment allocation. Show Remy's and Emile's indifference curves. (b) Derive the equation of the contract curve. In your graph in (a), draw the contract curve. (c) Set x1 as the numeraire, i.e., assume p, = 1 and p2 = p. Find the competitive equilibrium. Hint: For Emile to consume at a Paretoefficient allocation, what should the prices be? (d) Redraw the Edgeworth box. Indicate the equilibrium allocation, e. Draw the equilibrium budget line.Pete consumes goods 1 and 2. Pete thinks that 3 units of good 1 is always a perfect substitute for 4 units of good 2. Which of the following utility functions is the only one that would not represent Pete's preferences? A B D E U (x₁,x₂) = 40x₁+30x - 10000 2 U(x₁,x₂) = 4x₁+3x₂+ 1000 2 U (x₁,x₂) = min {4x₁, 3x₂} U(x,x)=16x² +24xx₂+9x² More than one of the above does not represent Pete's preferences.
