3. Christina loves pizza and hates burger. Her utility function is U(p – b) =p – →b´, | where p is the number of pizzas she consumes and b is the number of burgers she consumes. John likes both pizza and burger. His utility function is U(p, b) = p + 2\b Christina has an initial endowment of no pizzas and 8 burgers. John has an initial endowment of 16 pizzas and 8 burgers. a. Graph the initial endowment and label it E b. If Christina hates burgers and John likes them, how many burgers can Christina and John be consuming at a Pareto optimal allocation? What is John's marginal utility for pizzas and burgers? Mark the locus of Pareto optimal allocations of pizzas and burgers between Christina and John on the grapsh above.
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- Question 2 David spends his budget on chocolate and chip. His utility function is given by ?(?1,?2)= 2?1?2, where ?1 is the number of chocolates he consumers per week, and ?2 is the number of chips he buys per week. A chocolate costs 10 SEK, and a chip costs 20 SEK. David’s weekly budge for consuming on these two goods is 120 SEK. (1) What is David’s budge line? Draw the budget line on a graph with chocolate amounts on the horizontal axis and chip amounts on the vertical axis. Write explicitly at which points budget line crosses the axis. (2) What is David’s marginal utilities for the two goods, respectively? What is his marginal rate of substitution between the two goods? (3) What is David’s optimal choice? Calculate the numerical answer for the optimal bundle. Also draw an indifference curve for David on the same graph as question(1) and show the optimal bundle.of 55 The vending machine in Katherine's office building offers cans of pop and candies. Katherine's utility function is U = 3PC, where P is the amount of pop consumed per week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, she will consume10.6 For every two boxes of strawberries that she consumes, Millicent insists on having one pitcher of cream. She does not, however, insist on consuming the same amount every week. Her utility function is U = min{$₁,2c₁}min{$2,2c2} where s₁ and s2 are the number of boxes of strawberries she consumes this week and next week and c₁ and c₂ are the number of pitchers of cream she consumes this week and next. Strawberries cost $2 a box and cream costs $1 a pitcher. She has a present value of $100 to spend on these goods in the next two weeks. The weekly interest rate is 1%. How many boxes of strawberries will she consume this week? (a) 10 (b) 20 (c) 22 (d) 14.1 (e) 6.06
- Justin Barlow, a careful maximizer of utility, consumes only two goods, Krispy Kreme Doughnuts and coffee. He has just achieved the utility-maximizing solution in his consumption of the two goods when the price of Krispy Kreme Doughnuts falls by 50%. As he adjusts to this event, he will most likely * consume more of both Krispy Kreme Doughnuts and coffee consume less of both Krispy Kreme Doughnuts and coffee consume more Krispy Kreme Doughnuts and less coffee consume less Krispy Kreme Doughnuts and more coffee O consume the same amount of Krispy Kreme and coffeeJulio loves gardening. His favourite plants are tulips and hydrangeas. His utility function is ' u(t,h)= t +100h -h^2 where t is the number of tulipsin his garden and h is the number of hydrangeas in his garden. suppose he has a 500 square feet for his garden. each tulip takes up 1 square foot of space and each hydrangeas takes up 4 square feet. he gets both plants for free.If he wanted to maximize his utility, how many tulips should he plant, what about hydrangeas? b) if his yard was only 144 square feet, how many tulips would he plant? How many hydrangeas? C) In order to plant both tulips and hydrangeas, how big does his garden need to be. carfeully explain.Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is U(S,T) = 2ST, so MUs = 2T and MUT = 2S. It costs Linda $50 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $500 to spend on shoes and dancing. A. What is the equation for her budget line? Draw it (with T on the vertical axis) and label the slope and intercepts. B. What is Linda's marginal rate of substitution? Explain. C. Use math to solve for her optimal bundle. Show how to determine this bundle in a diagram using indifference curves and a budget line.
- Anne is going to the grocery store to buy some fruit. She can buy either apples or oranges. Let a be the quantity of apples she buys, and let zo be the quantity of oranges she buys. Her utility function is: u(xa, xo) = ln xa + 3 ln xo Anne has y pounds to spend. The price of apples is pa and the price of oranges is po (a) (b) Write down Anne's budget constraint and utility maximization problem, and the Lagrangian associated with this utility maximization problem. Find Anne's Marshallian demand functions for apples and oranges. Find Anne's indirect utility function.2. Jie has the utility function U, (a, b) = 2a + b and Daokui has the utility function U,(a, b) = v2ab, where a is the number of apples consumed and b is the number of bananas consumed. There are 10 units of apple and 10 units of banana in total. We draw an Edgeworth box with apple on the horizontal axis and banana on the vertical 4 axis and we measure Jie's consumptions from the lower left corner of the box. We assume that both apple and banana are infinitely divisible. Please answer the following questions. (a) Write down all pareto optimal allocations (you do not need to explain why). (b) If social welfare function is W min{U,(a, b), U(a, b)}, derive the social optimal allocation. Is this allocation pareto optimal? Suppose the endowment of Jie is 7 units of apple and 0 units of banana, and the endowment of Daokui is 3 units of apple and 10 units of banana. Please answer the following questions. (c) Assume that the price of apple is p, and the uniform price of banana is 1. Derive the…1 Consider a consumer who consumes only two goods, 21 and z2. His utility function is u (21, 22) = In z1 + 2. where In represents the natural logarithm. 1.a Derive the consumer's MRS of good 1 for good 2 using calculus to calculate his marginal utility from z and his marginal utility from z2. 1.b If the price of z1 is $2 per unit and the price of z2 is $4 per unit, and the consumer's income is $100, What is the equation of this consumer's budget line? 1.c What are the optimal consumption choices, z and z5, for this consumer? Show your work.
- Anne is going to the grocery store to buy some fruit. She can buy either apples or oranges. Let a be the quantity of apples she buys, and let zo be the quantity of oranges she buys. Her utility function is: u (xa, xo) = ln xa + 3 ln xo Anne has y pounds to spend. The price of apples is pa and the price of oranges is po When she gets to the grocery store, Anne realizes that she has forgotten her shopping bag. Without a shopping bag, she can carry at most 8 pieces of fruit. That is, it must be the case that xo + a ≤ 8. Suppose that the price of apples is pa = 1 and the price of oranges is p. = 3, and that Anne's income is y = 12. What is Anne's optimal consumption of apples and oranges?11) Stanley consumes only white and red wines and his utility function can be describedby U(R,W) = R0.40∙W0.60, where R is the number of bottles of red wine and W is the4number of bottles of white wine that he consumes per month. Suppose that his income is$500 and the price of a bottle of red wine $20 and the price of a bottle of white wine is$15. In this case, Stanley will purchase _____ bottles of red wine and _____ bottles ofwhite wine per month. Next, suppose that the price of red wine goes up to $35 per bottle.In this case, Stanley would consume ______ quantity of bottles of white wine comparedto the original situation.A) 10; 20; smallerB) 20; 10; smallerC) 10; 20; the sameD) 20; 10; the sameE) None of the above.Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2