An individual's utility function is given by U = 260x₁ + 310x₂ + 5x₁x₂ - 10x² – x² - where x₁ is the amount of leisure measured in hrs/week and x₂ is earned income measured in $/week. Find the values of x₁ and x2 which maximise utility.
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- TU = Total Utilityf= is a function ofMU = Marginal UtilityO = units of consumptionA= infinitesimal change EMV= Equimarginal ValueDigital 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…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. 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 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).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.Elisha is starting a tuxedo rental business and plans to charge $80 for the first day plus an extra $30 for each day beyond the first day. Create an equation for the income Elisha will receive where I stands for total income and D is the amount of extra days.
- Gina is at a toy store and is buying toy T-Rex's (x), which cost på, and toy yaks (y), which cost py. Her income is I. She likes 3 T-Rex's as much as she likes 4 yaks. These toys are perfect substitutes for her.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…What is the trend of the total utility
- True/False Marginal utility refers to the satisfaction or pleasure that occur due to the additional consumption of one more unitDefine Economic utilityAdrienne consumes three goods, x, y, and z. Her consumption preference is given by the utility function: u(x, y, z) = x*y} z#, (Pz-Py, Pz) where x, y, and z are the quantities she consumes (respectively). Let p = be the prices of the goods. Answer the following questions, and justify your answers carefully and mathematically. (a) Last year p = sumption bundle last year. (1, 10, 10) and Adrienne's income was 35. Find her optimal con- (b) This year, the prices of x and z have both risen 3.5% while the price of y has risen 7%, and Adrienne got an income raise of 3%. Find the (approximate) percentage changes of her consumption in the three goods due to these changes in prices and income. Does her raise adequately compensate her for the changed prices? What additional percentage change of her income would be needed if we were to restore Adrienne to last year's exact utility level?
