Assume x is beer and y is pizza and assume Caspar's utility function were Ulx, y) = min{8x, 4x + 16y}. Then, if the price of beer were $20 and the price of pizza were $60, Caspar would demand %3D O 3 times as much pizza as beer. only pizza O 6 times as much beer as pizza 5 times as much pizza as beer. 4 times as much beer as pizza.
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- Assume that Bob's utility function over beer x and pizza y is U(x,y) = 4x+12y. Which of the following statements is false? a) If the price of pizza is 12 and the price of beer is 3, then we can't determine how much pizza relative to beer Bob purchases. b) If the price of pizza is 16 and the price of beer is 5, then Bob only purchases pizza. c) If the price of pizza is 15 and the price of beer is 5, the own price elasticity of the demand for pizza as well as beer is infinite. d) It the price of pizza is 15 and the price of beer is 4, Bob purchases only beer e) Pizza and beer are perfect substitutes.Let x be the number of pizza slices and y the number of Cokes. If John’s utility function is u = min{7x, 4x+ 12y}, then if the price of pizza slices is 20 euros and the price of Coke is 40 euros, John will demand ? a- 2 times as pizza slices as Cokes b- 3 times as pizza slices as Cokes c- 6 times as pizza slices as Cokes d- 4 times as pizza slices as Cokes e- 5 times as pizza slices as Cokes f- only Cokes2. Tom spends all his $100 weekly income on two goods, apples and bananas. His utility function is given by U (A, B) = AB, where A and B stand for the quantity of apples and bananas consumed by Tom. If PA = $4 and PB= $10, how many apples and bananas will he consume? Make sure you write out the utility maximization problem explicitly, including the decision variable(s). What if his utility function is given by U (A, B) = A0.5B 0.5?
- Suppose that Omar’s marginal utility for cups of coffee is constant at 1.5 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 10 for the first doughnut he eats, 9 for the second he eats, 8 for the third he eats, and so on (that is, declining by 1 util per additional doughnut). In addition, suppose that coffee costs $1 per cup, doughnuts cost $1 each, and Omar has a budget that he can spend only on doughnuts, coffee, or both. How big would that budget have to be before he would spend a dollar buying a first cup of coffee?Suppose Karpov also enjoys eating nuts and berries. His utility function is u(c1,c2)=min{c1+2c2,2c1+c2}u(c1,c2)=min{c1+2c2,2c1+c2} where c1c1 is nuts and c2c2 is berries. However, Karpov faces different prices to Magnus. The prices he faces for nuts and berries are 3 and 2 respectively. Given his income of 10, how many units of nuts and berries does he consume? At what prices will Karpov only consume nuts and no berries? And, at what prices will he only consume berries and no nuts? Find all price and income combinations where Karpov will choose to consume equal quantities of berries and nuts.Mr Banda faces the following utility function from consuming nshima [X] and Rice [Y] U = 3XY 1 3 Mr Banda’s budget allocation for nshima and rice is K240. The price of nshima is K60 per Kg while that of Rice is K20 per Kg. A. How much nshima and rice should Mr. Banda consume to maximize his utility and What is the total utility at the optimum? b. What is the Lagrange multiplier? c. What will be the increase in utility when the budget allocation is increased to K241?
- A consumer has GH¢600 to spend on two commodities, A and B. Commodity A costs GH¢20 per unit and Commodity B costs GH¢30 per unit. Suppose that the utility derived by the consumer from x units of Commodity A, and y Commodity B is given by the Cobb-Douglas utility functionU (x, y) = 10x0.6y0.4a. How many units of each commodity should the consumer buy tomaximize utility?b. Is the budget constraint binding?PLEASE HELP ME ANSWER IT AS FAST AS YOU CAN Dalal consumes only two goods for lunch and dinner: risotto (R) and lamb machboos (M). Dalal’s utility function isgiven by U(R,M) = R + 4M. Suppose that a risotto dish costs 3 KD and that a dish of lamb machboos costs 6 KD.Dalal has 300 KD a month to spend on her lunch and dinner meals. a. How many risotto and lamb machboos dishes will Dalal buy each month if she maximizes utility?Dalal’s brother, Jassem, wants to make her happier and is considering two options: giving her a 60 KD gift card that can only be spent on risotto from one of the Italian restaurants or giving her some cash money.If Jassem chooses to give Dalal the 60 KD risotto gift card:b. How many risotto meals can Dalal add to her optimal basket? c. What utility level will Dalal get given her income and the risotto gift card?Suppose that Jassem instead chooses the second option and promises Dalal to raise her income to the level thatensures making her as happy as the first…Consider the following utility functions:Eleanor Rigby !" #, % = #%/10Father McKenzie !* #, % = 100#2%2;where # is one kilogram of apples and % one kilogram of bananas.1) Sketch all the bundles that Eleanor finds indifferent to having 8kg of apples and 2kg of bananas.2) Sketch all the bundles that Eleanor finds indifferent to having 6kg of apples and 4kg of bananas.3) Sketch all the bundles that Father McKenzie finds indifferent to having 8kg of apples and 2kg of bananas.
- Suppose Bilbo Baggins is deciding on whether to buy a sword or a bag of golden cups. If he has a utility function of U(C,S)= √(4C+S) and treasures amounting to 200, while the prices of the sword and bag of golden cup are 4 coppers and 5 coppers, respectively, how many swords and bags of cups can he buy?Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice cream sundaes (z)− according to the Cobb-Douglas utility function U(x,y,z)=x0.5y0.5(1+z)0.5. Suppose also that the prices for these goods are given by px=1,py=4, and pz=8 and that this consumer's income is given by I=8.a. Show that, for z=0, maximization of utility results in the same optimal choices as in Example 4.1 . Show also that any choice that results in z>0 (even for a fractionalz ) reduces utility from this optimum.b. How do you explain the fact that z=0 is optimal here?c. How high would this individual's income have to be for any z to be purchased?John has a utility function u(x,y)= min{0.5x,1.5y} , for baskets containing the goods x and y. What is John's utility if he consumes a basket where (x,y) = (20,8) ? a. 4.5 b. 8 c. 10 d. 12