Two students go out to lunch and decide to split the bill evenly between them. Each student has a quasi-linear utility function given by ui(fi , xi) = φi(fi) + xi , where φi(·) is strictly concave, fi is the amount of food consumed by student i, and xi is a composite numeraire good. Each student has a fixed budget of mi . EVALUATE THIS CLAIM: Both students eat too much!
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Two students go out to lunch and decide to split the bill evenly between them. Each student has a quasi-linear utility function given by ui(fi , xi) = φi(fi) + xi , where φi(·) is strictly concave, fi is the amount of food consumed by student i, and xi is a composite numeraire good. Each student has a fixed budget of mi . EVALUATE THIS CLAIM: Both students eat too much!
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- If Ginna spends her entire budget, she could buy a chosen set of groceries and also buy 10 notebooks. If she spends only half of her budget, she could only buy a set of groceries and could not afford any notebooks. Suppose Ginna's budget is £150. Her preferences for groceries (G) and notebooks (N) can be described by the following utility function: U (G, N) = 30G + 2N (MUG = 30, MUN = 2). a) Find Ginna's optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how the price of a notebook should change for Ginna to change her optimal consumption choice. c) If the price of a notebook increases by 50%, how should the price of the groceries drop so that Ginna can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ginna's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ginna's demand for groceries and/or notebooks.Two grad students go out to lunch and decide to split the bill evenly between them. Each student has a quasi-linear utility function given by ui(fi, xi) = φi(fi)+xi, where φi(·) is strictly concave, fi is the amount of food consumed by student i, and xi is a composite numeraire good. Each student has a fixed budget of mi. EVALUATE THIS CLAIM: Both students eat too much!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)
- Maya is doing her undergrad at Queen's University. She loves donuts and chocolate chip cookies (CCC). Her utility function is given by u(x, y) = √8x +5 + 2y, where x denotes her consumption of donuts and y denotes her consumption of CCC. Her budget is $10/day. The price of a donut is $1. (a) When the price of CCC is $1, what is Maya's optimal choice of donuts and CCC? (b) When the price of CCC is $8, what is Maya's optimal choice of donuts and CCC? (c) When the price of CCC increases from $1 to $8, calculate Maya's substitution effect and income effect. (d) According to your calculation in part (c), is CCC a normal good or an inferior good? Explain. Is CCC an ordinary good or a Giffen good? Explain.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.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
- Mort consumes only beer and sausages. His income is $100. Beer costs him $0.50 per can and sausages cost $1 each, where x is the number of cans of beer and y is the number of sausages he consumes per week. Mort’s utility function is U(x,y) = -[(x-50)^2 + (y-40)^2]. What consumption bundle should he have?Penny likes to have peanut butter (B) with apples (A). The price of apples is $3 per pound and peanut butter costs $.50 per ounce. Penny's budget for peanut butter and apples is $3.60. Penny's utility function is U (A, B) = A/B. Penny's MRS is [ Select ] His income expansion path is described by [ [ Select ] . Thus, Penny will consume [Select ] ounces of peanut butter and [ Select ] pounds of apples.A consumer has set a budget of $400 for the consumption of good X and Y. The price of Good X is S"Px", and the price of good Y is S5. The consumer has a Utility function given by U(X,Y) = ху Find the optimal consumption choice of the individual and the utility obtained in terms of Px. Make a graph that illustrates the solution to the problem. Why do we use parameters?
- Jackie has a budget of $36 per month to spend on snacks. She can spend this budget on bags of potato chips (C) and Hershey chocolate bars (H). Potato chips cost $4 per bag, while Hershey bars cost $1 per bar. The utility that Jackie receives from consuming potato chips and Hershey bars is represented by the following utility function: U=3C2 H. Given that Jackie seeks to maximize her utility, find the number of potato chip bags and Hershey chocolate bars that Jackie will purchase each month.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 What is the equation for her budget line? Draw it (with T on the vertical axis), and label the slope and intercepts. What is Linda’s marginal rate of substitution? Explain. Use math to solve for her optimal bundle. Show how to determine this bundle in a diagram using indifference curves and a budget lineJulio 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.