Suppose further that there are only two individuals in the economy, A and B, and their utility function is given as: U(XAYA) - XA0YA0.8, U(XBYB) = XB0.8YB0.2 Deriving the required condition for efficiency (or the contract curve equation) for consumer A (XAYA), the MRSxy^= MRSXY³ equation leads to YA [ Select] The required efficiency equation is XA = [Select] given that the economy has 10 units each of goods X and Y.
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- 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 ecoFrom economic theory, the willingness of a consumer to give up consumption of one commodity (X) in exchange for an increase in some other commodity (Y) and remain equally satisfied can be mathematically calculated as their marginal utility of good X divided by their marginal utility of good Y. What is the economic term for this measure or concept?Please refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by Your marginal utility function for apples is . Your marginal utility function for oranges is U (A, O) = AO³ 2 apples, 28 oranges 3 apples, 26 oranges MUA 4 apples, 24 oranges 5 apples, 22 oranges 8 apples, 16 oranges 9 apples, 14 oranges MUO 3A0² . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. : 0³ - = Given your preferences and budget constraint, what bundle represents your consumer equilibrium for apples and oranges?
- Please refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by Your marginal utility function for apples is . Your marginal utility function for oranges is U (A, O) = AO³ MUA = 0³ MUO 3A0² . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. = When you set up the optimal decision rule for your consumer problem, which of the following statements best describes how much you will buy of apples and oranges at your consumer equilibrium? For each peck of apples, you will buy 1/3 pounds of oranges. For each peck of apples, you will buy 1 pounds of oranges. O For each peck of apples, you will buy 3 pounds of oranges. O For each peck of apples, you will buy 6 pounds of oranges.Suppose Kayla has preferences over cakes (c) and pints of ice cream (i) that can be characterized using the utility function u (c, i) = √ci. Kayla is currently in possession of 2 cakes and 4 pints of ice cream. If you offered to trade her one cake for some ice cream, how many pints would she be willing to give you?Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: UA (XA,YA) = X0.25Y0.75, UB (XB,YB) = X0.75Y 0.25show the MRS equation and find the required efficiency equation in XA
- Rafe is optimally choosing to consume 6 apples and 3 bananas. The prices of apples and bananas are p. = 7 and pb - 7. Which of the following utility functions over quantities of apples (a) and bananas (b) could represent Rafe's preferences? = u(a, b)-a4/5 61/5 Ou(a, b) = a¹/5 64/5 Ou(a, b)-a2/3 b1/3 Ou(a, b)-a¹/3 2/3If the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.While visiting family in Mexico, your professor has a budget of $ 255 ($ = pesos) that he spends on tacos and tequila. The price of tacos is $ 6 and a shot of tequila is priced at $ 16. During his visit the price of tacos changes to $ 5. Assume your professor has a Cobb-Douglas utility function with (tacos) parameter a = ( 27 / 100). How many shots of tequila does your professor purchase ? (Assume both goods are commodities.) (Answer is : 11.63)
- For the utility function U = Qx^0.84Qy^(1-0.84) rate between good X and good Y at Qx= 7 and Qy=19 find the trade-offI am unsure the direction the utility functions would go in , with this specific scenarioPlease refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by Your marginal utility function for apples is . Your marginal utility function for oranges is 2 apples, 10 oranges 2 apples, 11 oranges 4 apples, 12 oranges U (A, O) = AO³ 5 apples, 13 oranges 6 apples, 14 oranges MUA 0³ MUO . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. Let's say the price of oranges rises to $10/pound of oranges. Given your preferences and budget constraint, what bundle represents your new consumer equilibrium for apples and oranges? = = 3A0²