Diogo has a utility function, U(91, 92)=910.59₂0.5 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 $2.50, and income, Y, is $100, what is Diogo's optimal bundle? The optimal value of good q₁ is 91 units. (Enter your response rounded to two decimal places.)
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- Diogo has a utility function, 0.2, 0.8 where g, is chocolate candy and g, is slices of pie. If the price of slices of pie, p2, is $1.00, the price of chocolate candy, p.. is $0.50, and income, Y, is $100, what is Diogo's optimal bundle? The optimal value of good q, is 9, = units. (Enter your response rounded to two decimal places.) Cha 15 tv MacBook Air 80 esc DD F1 F2 F3 F4 F5 F6 F7 F8 F9 ! @ 23 $ % & 3 4 7 8 Q W E R T Y tab A S F G J caps lock Z C V B mift fn control option command つ エ く6 ピQ5. Jason has preferences defined over novels (good x) and DVDs (good y) described by the utility function U(x,y)= x2y2. He has an income of $120; novels cost $5 each, while DVDs are priced at $15 each. [Hint: MUx=2xy2, MUy=2x2y] a) Sketch Jason's budget constraint, indifference curves and the interior solution in a graph. b) Calculate Jason's optimal consumption bundle, and his maximized utility level. Suppose the price of novels increases to $7.5, while the price of DVDs and income are unchanged. c) Calculate his new optimal bundle, show it in the same graph from a), and interpret the Marginal Rate of Substitution (MRS) at this new optional bundle (point).A consumer’s preferences over pizza (x) and steak (y) are given by u(x,y) = x^2y (HINT: MUx = 2xy and MUy = x2) and his income is I = $120 and py = $1. (a) Calculate his optimal bundle when pX = $8 (call this bundle A) and separately when pX = $1 (call this point C). (b) Finding the decomposition bundle B, calculate the income and substitution effects on the amount of pizza of a decrease in the price of pizza from pX = $8 down to pX = $1. (c) Forget about the decomposition bundle and the two effects. In (a), the price of pizza decreases, hence the agent ends up better off. Let’s quantify how much “better off” the agent becomes after this price drop, in dollars. For this, instead of the price drop, suppose the agent is given some money $m and he optimize utility with this additional gift included to his budget. What should m be, so that his optimal utility with his expanded budget is exactly equal to his utility at the bundle C (the bundle he chooses optimally when pizza price drops to…
- Suppose that U(f,c) = f + 8c^(1/2)is a utility function that describes Amelia’s preferences over two goods: fish(f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis.a. Derive an expression for her marginal utility (Uf)from a small increase in f holding c fixed. Also find themarginal utility for custard (Uc).b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitivedescription of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, howmany units of custard would she be willing to give up in order to get one more unit of fish?c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goodson the indifference curve.d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5properties of indifference curves? Briefly support your answer.e. Give another utility function that represents…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)Lan's utility function is U (x,y) =6.9 x².9y7.4. If the price of good X is 8.3 and Lan's optimal bundle has x*-9 units of good X and y*=1.1 units of good Y, what is the price of good Y?
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