(1) Draw an Edgeworth box and show the initial allocation of goods, to be labelled e. Indicate the initial quantities of each person's goods on the four axes.
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- Donna and Jim are two consumers purchasing strawberries and chocolate. Jim’s utility function is ?(?,?) = ?? and Donna’s utility function is ?(?,?) = ?2? where x is strawberries and y is chocolate. 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, andDonna’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?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)Krissy spends all her income on holiday lights (L) and fishing bait (B). Lights are priced at $2, while a pack of bait costs $1. Assume that Krissy has $30 to spend and her utility function can be represented as: U(L,B) = L²B² with: MU=2LB² and MU=2L²B (Assume B is on the y-axis when graphing). How much utility does Krissy obtain from the optimal bundle? Note: enter number(s) only and convert any fraction to a decimal.
- Logan consumes olives (x₁) and ice cream (x₂). He prefers to eat them only separately (never together). In particular, his utility function is given by: u(x₁,x2)= x₁²+x₂². If his income is $10 and the price of olives is $1 and the price of ice cream is $2. Which of the following is FALSE? The optimal bundle Logan will choose to consume is (2,4) None of the above The utility level at a bundle (2,4) is 20 The utility level when he spends all of his income on good 1 is 100 The utility level when he spends all of his income on good 2 is 25uestion1: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 ecoConsider the following scenario: Ahmad dislikes plain coffee, unless he eats something sweetie with the coffee. In particular, he likes to consume Starbuck's coffee (X2) only if he is compensated by one caramel doughnut (X,) while drinking the plain coffee. Otherwise, drinking plain coffee is not desirable for him. Ahmad has budget M, Ahmad's target utility is U = K, the marginal utility of one doughnut is A, and his marginal disutility of one plain coffee without doughnut is “– B". A. Write down Ahmaď's consumer optimization (objective and constraints). B. Derive Ahmad's demand functions for plain coffee (X2) and doughnuts (X,). C. What is Ahmad's maximum utility? D. Get the compensation inequality condition. E. Find the minimum compensation required for Ahmad to consume Starbuck's plain coffee. F. Show graphically.
- 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 2/3John spends all his money on leather jackets and hats. John’s utility function is given by U(x1, x2) = min{4x1,2x1+x2} where x1is the consumption of leather jackets and x2 is the consumption of hats. Suppose that John is making an optimal choice, and he consumes at the point (x1= 15, x2= 10). Moreover, the price of leather jackets (per unit) is $10. 1. Graph the indifference curve that passes through the point (15,10). 2. What must be the price of hats? 3. What is john’s total income?Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U(D,F)= 10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane's annual travel budget is $4000. An indifference curve associated with a level of utility equal to 800 and an indifference curve associated with utility of 1200 are illustrated in the figure to the right. Using the line drawing tool, graph Jane's budget line. Label this line L,. Carefully follow the instructions above, and only draw the required object. Can Jane afford any of the bundles that give her a utility of 800? Can Jane afford any of the utility bundles that give her a utility of 1200? Find Jane's utility-maximizing choice of days spent traveling domestically and days spent in a foreign country. days of domestic travel and days of foreign travel. (Enter…
- QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x2). Linguini has utility function UA = x4x4 and Colette has utility function UB = 2xfx. Linguini is endowed with 10 éclair (x,) and 3 profiterole (x), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x2). (a) Draw an Edgeworth box with x, on the horizontal axis and x, on the vertical axis. Position Linguini on the bottom left corner and Colette on the top right comer. Indicate the total number of units of x, and x2. Label the endowment allocation. (b) Derive the equation of the contract curve, ie., find x(x). In your graph in (a), draw the contract curve.Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…Tom went to a pizza by the slice bar with Jerry. Tom loves pizza (x), and prefers it, even more, when he can eat them with Coke (y). While Jerry is super hungry and will devour any amount of pizza and Coke available to him, Tom knows that there is a sweet spot for him, that is, an amount of pizza and Coke that maximizes his satisfaction. Tom’s preferences are represented by the utility function: u(x,y) = min{5,min{x,2.5y}}Tom took $30 with him to the pizza joint, and when he got there he saw the prices for a slice of pizza or a cup of Coke were $3 and $1.50, respectively. a.) What is Tom’s budget constraint? b.) How many slices of pizza and cups of Coke will Tom choose, in order to maximize his utility? Also, how much money does Tom uses? Assume Tom will not spend any money that does not increase his utility. c.) If Jerry needed money from Tom, what is the most money Tom can lend him? Explain.
