A consumer has the following utility function: U(X,Y)= 400X2/5Y3/5 Suppose that the price of a spa day (x) is £200 and the price of a city break (y) is £300 Find the number of spa days and city breaks that minimise expenditure if 12,800 units of utility are obtained. Also calculate the consumer's minimised expenditure
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A consumer has the following utility function: U(X,Y)= 400X2/5Y3/5
Suppose that the price of a spa day (x) is £200 and the price of a city break (y) is £300
Find the number of spa days and city breaks that minimise expenditure if 12,800 units of utility are obtained.
Also calculate the consumer's minimised expenditure
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- Define Economic utilityEren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should begiven to Eren to offset his change un utility due to the price increase of an expensivemeal. Calculate the compensative variation (CV).Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate for the equivalent variation (EV) for the price change.
- Max is very peculiar about his morning coffee routine. He likes to use exactly two spoons of coffee for every six ounces of water. This give him the following utility function: U = min(2Water, 6Cof fee), where Water (W) is measured in fluid ounces and Coffee (C) in spoons. (a) afford while utility-maximizing? How many spoons of coffee does he use in doing so? (b) If he spends exactly $2 on coffee every morning, how many 8 ounce cups of coffee can he How much utility does Max get from his morning cup/s of coffee?Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).EXERCISE 7 Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L, P) = 3L + P. (MU₁ = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so…
- Digital Apps per Period 0 1 2 3 4 5 Total Utility of Digital Apps per Period (utils) which 0 50.0 95.0 135.0 171.5 200.0 Marginal Utility (utils) 50.0 45.0 40.0 36.5 28.5 Marginal Utility Portable per Dollars Spent Power Banks (price = $5.97) per Period | 8.4 7.5 6.7 6.1 4.8 0 1 GTA W N 3 4 5 Total Utility of Portable Power Banks per Period (utils) 0 25 47 65 80 89 Marginal Utility (utils) 25 22 18 15 9 Marginal Utility per Dollars Spent (price = $2.70) 9.3 8.1 6.7 5.6 3.3 Consider the table above. Suppose the consumer's income is $26. Does the consumer spend all of her income if she purchases the optimal quantities of digital apps and portable power banks? The optimum quantity of digital apps purchased is and the optimum quantity of portable power banks purchased is. (Enter your responses as whole numbers.) Spending on digital apps is $ and spending on portable power banks is $. (Enter your responses rounded to one decimal place.) Thus, total spending at the consumer optimum is $ the…Distinguish between cardinal and ordinal utilityFor each of the following utility functions get the marginal utility of consumption of each of the goods. 1/2 1/2 (a) u(a,b) = a b (b) u(x, y) = x³/4y1/4 (c) u(a, b) = n(a) + In(x) (d) u(x, y) = ln(x) + ln(y) (e) u(a, b) = 2xa +Xb
- Consider the following utility functions. G(x,y) = -1/[ min (6x, 2y)+1] H(x,y) = min (6x,6y) L(x,y) = min (6x,2y) - 10000000000 U(x,y) = min (3x, y) W(x,y) = min (6x, y) Z(x,y) = min (x,2y) Select the function or functions, if any, representing the same preferences as function U?EXERCISE 6 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.1. Pindyck and Rubinfeld (2018) Chapter 4 Appendix, Exercise #5 Jae has the following utility function: U(X,Y)= 20X+ 80Y – X² – 2Y?, where X is consumption of CDs, with a price of $1, and Y is consumption of movie videos, with a rental price of $2. Jae plans to spend $41 on both forms of entertainment. Determine the number of CDs and video rentals that will maximize Jae's utility. а.