Diogo has a utility function, U(q1, q2) = q1^.8q2^.2, where q1 is chocolate candy and q2 is slices of pie. If the price of slices of pie, p2, is $5.00, the price of chocolate candy, p1, is$10.00, and income, Y, is $100, what is Diogo's optimalbundle? The optimal value of good q1 is?
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- Consider a utility function l(X_{A}, X_{B}) = X_{A}*X_{B} Let P_{A} =\$3 and P_{B} =\$2. and income is set at M =\$40. Suppose P_{B} falls to P_{B}' = 1 1. Before the price change, what was x_{A} ^ * and x B^ * the optimal consumption bundles? Sketch the original budget line and label the point ( x_{A} ^ * ,x B ^ * ) as A. Let x_{A} be on the horizontal axis. 2. If, after the price change, income changed so that the original optimal bundle is just as affordable. What is the new income, m' ? At (p_{A}, p_{B}', m') what is the new optimal bundle (x_{A}', x_{B}')' Sketch the budget line associated with p_{A}, p_{B}', m' ) . Label the point (x_{A}', x_{B}') as B. 3. Does the substitution effect result in more x_{B} ? How many more or fewer? 4. After the price change, how much x_{A} and x_{B} are actually bought. ( x_{A} ^ prime prime ,x B ^ prime prime )? Sketch the budget line associated with (p_{A}, p_{B}', m) Label the point x_{4} ^ prime prime , x_{R} ^ prime prime ) as C. 5.…The utility function of a consumer regarding two goods x and y is given byU(x,y) = x^(7.9)y^(9). Good x costs 19, and good y costs 80 units of money. The consumer's entire budget is 10800 units of money. How much is her optimal consumption of the good x?Recall that Casper's utility function is 3x + y, where x is his consumption of cocoa and y is his consumption of cheese. If the total cost of x units of cocoa is x2, the price of cheese is $8, and Casper's income is $184, how many units of cocoa will he consume?
- Consider the utility functions below of two individuals, A and B, and bundles of goods Q and R. UA=X0.5Y0.5; UB=X+2Y; Bundle Q (10, 10); Bundle R (10, 15). Suppose the total X and total Y available in the economy are both equal to 20. a. If initially both individuals are consuming bundle Q, then a pareto-improvement is possible through reallocation of goods, i.e. individual A gives B some of his good X in exchange for some of individual B’s good Y. (True or False? Explain through mathematical examples).b. Pareto-optimality is achieved if we give individual B Bundle R and the remaining goods X and Y available in the economy is given to individual A. (True or false? Explain through a graphical example)Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F Suppose as Case 1, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $15, respectively, then: a) What is the value of MRS at the optimal point and what does this value mean? b) What is the optimal consumption bundle i.e (F*,C*)? c) Also plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) spaceJane 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. Suppose F is on the horizontal axis and D is on the vertical axis. Jane's marginal rate of substitution between F and D is equal to 10 1 F/D D/F
- Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F Suppose as Case 1, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $10, respectively, then: a) What is the value of MRS at the optimal point and what does this value mean? b) What is the optimal consumption bundle i.e (F*,C*)? c) Also plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space Now assume a new Case 3, where instead of one time income change, Pc' = $15, holding all else the same as in Case 1, do the same analysis (parts a-c) and contrast your answers to Case 1. For part c, you should draw old (Case 1) and new (Case 3) budget lines/point of optimality.Please answer and explain case 3 and draw draw old (Case 1) and new (Case 3) budget lines/point of optimality.Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F Suppose as Case 1, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $10, respectively, then: a) What is the value of MRS at the optimal point and what does this value mean? b) What is the optimal consumption bundle i.e (F*,C*)? c) Also plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space Case # 2 assuming if income increases to $120, holding all else the same, do the same analysis (parts a-c) and contrast your answers to Case 1. For part c, you should draw old (Case 1) and new (Case 2) budget lines/point of optimality.Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F Suppose as Case 1, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $10, respectively, then: a) What is the value of MRS at the optimal point and what does this value mean? b) What is the optimal consumption bundle i.e (F*,C*)? c) Also plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space Case # 2 assuming if income increases to $120, holding all else the same, do the same analysis (parts a-c) and contrast your answers to Case 1. For part c, you should draw old (Case 1) and new (Case 2) budget lines/point of optimality.Please answer and explain case 2 and compare their budget lines/point of optimality.
- Mike has two identical brothers. Each of them have the same utility function below. If Mike and his brothers are the only people in the market, what is the aggregate demand at each price of X below? (Each of their income is $100 and the price of Y is always $1). U (x,y) = x^2/5 Y^3/5 Price of X=$8 Price of X=$4 Price of X=$2 Price of X=$1Suppose Anna’s utility for goods x1 and x2 is represented by the following utility function: U (x1, x2) = x11/2 x21/2 (a) Find Anna’s marginal rate of substitution, MRS12.(b) If the price for good x1 is p1 = 1, the price for good x2 is p2 = 2 and Anna’s available income is m = 12, write down Anna’s budget constraint. (c) For the utility, prices and income given above, find Anna’s optimal consumption choice (Marshallian demand) and her utility level.The optimal quantity of a product A in an optimal bundle (of products A, B, C,..., etc.) will be where the marginal benefit ( MU) of the optimal quantity of A is equal to the marginal cost ( P) of the product A. True or False?
