Suppose that the endowments are the same as in the slides: (,)-(6,4) and (ww)-(2,2). Suppose that the utility functions are U^(₁,2)- and U"(",)=(s). Find the contract curve, the Core, and the equilibrium.
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- Refer to figure. Suppose the consumer is endowed with 10 units of orange and consumes 5 units of apple. The price of the apple decreases and at the new price the consumer consumes 9 units of apple. The change in the demand for apples due to the endowment effect is equal to Optionsa) 3b) 4c) 1d) none of these1 Consumption utility functions Consider the following utility functions defined over the outcome space X = R². 1. U(1, ₂) = 1X2 2. U(1, ₂) = 2x₁ + x₂ 3. U(1, 2) = min{2x1,4x2} 4. U(₁, ₂) = 100 - (₁ - 10)²(x₂ - 10)² 5. U(x₁, x₂) = 1 + ln(x₂ + 1) 6. U(x₁, x₂) = x² + x² For each function: (a) Draw two indifference curves and an arrow indicating the direction of increasing prefer- ence. (b) Shade the upper contour set above the more-preferred indifference curve you drew in the previous part. (c) Indicate which of the following properties are satisfied by the underlying preference relation: convexity, monotonicity, local nonsatiation. (A given preference may satisfy more than one!) Explain why each property does or does not hold.Suppose the function for the utility from good c is denoted as U(c)=2c2. Which of the following expressions indicates the marginal utility of c? 1/c2 1/square root of c All of the above are correct.
- Zeynep is at the supermarket buying her bi-weekly groceries. As she arrived at the store right before closing, not much is left on the shelves; so her purchases are limited to beef, B, and an assortment of organic vegetables, V. Beef costs £50/kg and vegetables Ł10/kg. Her utility function is expressed as U(B,V) = B0-6v0.3. She has ±150 to spend. Please answer the following questions using this information: A) Given the vegetables cost less than beef, explain why Zeynep would not only buy vegetables. B) Write Zeynep's constrained maximization problem (objective function subject to her budget constraint). C) Using the Lagrangian technique, find how much beef and vegetables would Zeynep buy? D) Show that for the preferences represented as above, demand for beef is a function of only its own price, pg, and income, m, but not the price of vegetables, py. Note: Rather than using the given prices and income, use PB, Py and m. Find and comment on the comparative statics, i.e., how do changes…Given the utility function U (x1, x2) = x³x2.7 select all that are true. a) 30% of the budget is spent on good 1. ○b) V (p, I) = 30.370.7 I 10 P1P2 c) If P2 = 2 and I = 60, then $18 is spent on good 21. d) If P1 = 9, P2 = 2, and I = 60 then the consumer enjoys 1.81 utils of utility. e) Half the budget is spent on good 1 and the other half is spent on 2.Consider the following utility functions: a) U= xy b) U=(xy)l3 c) U=min(x,y/2) d) U=2x + 3y e) U=x?y? + xy 1. Check if any of utility functions a) – e) are homogeneous. If so, state the degree of homogeneity of each.
- Katalin has the utility of U(x 1, x 2 ) = max{3x 1, 4x 2 } of purchasing products 1 and 2. Katalin has an initial endowment of ( ω 1,ω 2 ) = (40,40), and initial prices are 2 and 5 forproducts 1 and 2, respectively. When prices change and 3$ for both products, find the pure substitution, income, and endowment effects for Katalin.2) For the following utility functions, using the budget constraint M = Pxx & Pyy, find the compensated (Hicksian) demand functions. Note: For a, minimize expenditure; For b, maximize utility and use the Shepard's Lemma. a) U(x,y) = x0.5 + 2y0.5 b) U (x, y) = min{2x, 5y}There are 6 cups of espresso (x1) and 6 bars of chocolate (x2) in the house. Andrew and Eric have identical preferences, U₁ = alog(x) + (1 - a)log(x), where i = A, E and a € (0, 1). Suppose the Target allocation is ((2, 2), (4, 4)). (a) What is the relationship between UA and UE in the Target? (b) Find the ratio of equilibrium prices at the Target allocation. (c) Determine the lump-sum transfer necessary to achieve the Target if An- drew is initially endowed with (4, 1) and Eric with (2,5). Set x2 as the numeraire, i.e., assume pi 1. Under what condition would require Andrew to transfer to Eric or vice versa? Why? If a > 1/3, Andrew transfers to Eric and vice versa. = p and p2 =
- Alex's utility is U (xA, YA) = min {TA, YA}, where zA, and y, are his consumptions of %3D goods a and y respectively. Becky's utility function is U (zB, YB ) = TBYB where ap and yp are her consumptions of goods a and y. Alex's initial endowment is 20 units of x and 12 units of y. Becky's initial endowment is 12 units of x and 20 units of y. At the Walrasian equilibrium, a) Both of them consume 16 units of good y each. b) Alex consumes 8 units of good y and Becky consumes 16 units of y. c) Both of them consumes 12 units of good x each. d) Alex consumes 12 units of good x and Becky consumes 20 units of x. e) None of the aboveQ2. Suppose a consumer seeks to maximize the utility function U (x, y) = (x + 2) (y + 1), where x and y represent the quantities of the two goods consumed. The prices of the two goods and the consumer's income are pa, py, and I. (c) Show the bordered Hessian matrix, H for this problem. What does the second order condition require for this problem? Show if it is satisfied.For the utility function U = Qx0.31Qy(1-0.31) find the trade-off rate between good X and good Y at Qx= 7 and Qy=17 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).