UA(XA. YA) = 4XA + 3YA UB (XB. Ya) 5(X)^ (Y₂)² Q1 a) Suppose that initially consumer A has 5 units of X and 15 units of Y, and that consumer B has 15 units of X and 5 units of Y. Is this allocation Pareto efficient? Let Px and Py be the prices of goods X and Y, respectively. Write down expressions for the two individuals' budget constraints.

Ginny likes to eat Bertie Bott's Every Flavour Beans (b), and Chocolate Frogs (f). Her preferences over these lollies are Cobb-Douglas, and can be presented by the utility function u(b, ƒ) = (b − 2)(ƒ +3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frog costs 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectly divisible goods. (a) Find Ginny's optimal bundle. (b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the time she is there, she is left only with 75 Knuts. What is her optimal bundle now? (c) Now, consider the general case, where Ginny's income is m, the price of Every Flavour Beans is po, and the price of Chocolate Frogs is given by pf. In other words, treat Chocolate Frogs as the numeraire. Find Ginny's demand for each good in terms of m, p and Pf. (d) Find the good on which Ginny will always spend more than half of her income. (e) Find the own-price, cross-price, and income elasticities of good…

Suppose there are two firms selling protein bars. Firm 1 sells 'AggieBars' with 10 grams of protein and firm 2 sells 'DavisBars' with 20 grams of protein. Consumers are distributed uniformly over their preferences for grams of protein between 10 and 20. Suppose firm 1 sells AggieBars for $2 and firm 2 sells DavisBars for $3. The 'cost to consumers of deviating from their optimal amount of protein is $0.20 per gram. a. What protein content does the marginal consumer (the consumer who is indifferent between AggieBars and DavisBars) prefer? The equation for finding the marginal consumer (when the range of product attribute values is 10) is V - p1 - tx m = V – p2 – t(10 – x m) 4 b. How would the proportion of consumers buying each product change if the cost to deviation from one's optimal amount of protein increased (was greater than $0.20 per gram)?

Suppose the utility possibility frontier for two individuals is given by   U_a+2U_b=200   Please plot the utility frontier on a graph.

Divya and Emily have to divide a bag of 200 pistachios between them. They derive enjoyment from pistachios according to the following hedonic utility functions: uD(x) = √x for Divya; uE (x) = 2√x for Emily (where x is the number of pistachios eaten). (a) Consider all possible ways of dividing the pistachios. Treating the utilities given above as the two agents" "levels," which division is best according to the utilitarian criterion? (b) Which division is best according to the leximin criterion? (c) Which is best according to the Nash criterion?

Q2. 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.

Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 9 units of X and a TOTAL of 9 units of Y. The consumers' utility functions are given by: UA(X,Y) = 3X + Y UB(X,Y) = X2 Y For Each of the following allocations, answer True if it is Pareto Efficient, and False if it is not Pareto Efficient. [ Select ] Allocation A: Consumer A gets X = 7 and Y =6; Consumer B gets X = 2 and Y = 3. [ Select ] Allocation B: Consumer A gets X = 6 and Y =7; !3! Consumer B gets X = 3 and Y = 2 %3D [ Select ] Allocation C: Consumer A gets X = 2 and Y =0; Consumer B gets X = 7 and Y = 9 [ Select ] v Allocation D: Consumer A gets X = 1 and Y =0; Consumer B gets X = 8 and Y = 9

please teach   solve explain step by step

For the case of two goods, give an example of a utility function U(x1, x2) that represents the preferences of a consumer who regards the two goods as perfect complements. Next, take the transformation f(U) = U³ of the your example utility function and explain if this newly gener ated function represents the original preferences. Further, provide clear arguments supporting or rejecting the claim that "f(U(x1, x2)) must be strongly increasing in (x1, x2)."

Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. Consumer A is initially endowed with 10 units of good 1 and 10 units of good 2. Consumer B is initially endowed with 2 units of good 1 and 2 units of good 2. The consumers have the following utility functions: ua(X1a,X2a)=X1AX2A²; uB(x1B,X2B)=X1B+X2g. Among the prices below, which ones are Walrasian equilibrium prices? O a. p1=3, p2 =2 O b. p1=4, P2 =5 O C. None of the other answers. O d. p1=5, p2 =4 O e. P1=2, p2 =3