Questions 1. Will's utility from vacations (91) and meals (92) is given by the function U(V, M) = 91 x 92. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, while the price of vacations remained the same. Both years, Will had an income of $1500. (a) What is the compensating variation for the price change in meals? (b) What is the equivalent variation for the price change in meals?
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- Kamau's utility function for watching football (F) and drinking a soda (S) is given by the function (F,S)=F°S . Last month, the price of a football ticket was Ksh.100 and the price of Soda was Ksh.25. This month the price of soda has risen to Ksh.37.5, the price of a football ticet has remained the same. For both months, Kamau's income has remained to be Ksh750. Calculate Kamau's CS, CV and EV.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 for the equivalent variation (EV) for the price change.
- 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.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).2nd attempt Greg has the following utility function: u = x0.55x0.45. He has an income of $96.00, and he faces these prices: (P1, P2) (10.00, 8.00). Suppose that the price of x₁ increases by $1.00. Calculate the compensating variation for this price change. Give your answer to two decimals. $ =
- Brian spends his entire monthly income of $1200 on shoes (S) and pizzas (P). The price of a pair of shoes is $60, and the price of a pizza is $20. If he consumes 10 pairs of shoes and 30 pizzas, his MRS is 2P/1S. (A quantity of shoes is measured along the x-axis, and a quantity of pizza is measured along the y-axis.) His choice is optimal. True FalseEXERCISE 2 Consider a consumer who consumes two goods and has utility function u(x₁, x2) = x2 + √₁. The price of good 2 is 1, the price of good 1 is p, and income is m. Start with m = 10 and p = 1.5, and suppose that the price of good 1 increases by 25%. Compute the substitution and the income effect.3. U(X,Y)= X¹/2Y1/2 M = $36: Py = $1; Px is initially = $1; the price of Good X increases to Px = $9. 4. U(X,Y)= X1/2Y1/2 M = $64; Py = $1; Px is initially = $16; the price of Good X decreases to Px = $1.
- Question 6 A consumer spends all of her income on two goods, coffee and doughnuts. She buys coffee at 25 cents per unit with a total utility of 800 and a marginal utility of 12. Doughnuts are purchased at 75 cents a unit with a total utility of 200 and a marginal utility of 24. To increase her total utility, the consumer should: Buy more coffee and less doughnuts Buy more of both goods Do nothing. She is currently maximizing utility with her limited budget. Buy less of both goods Buy more doughnuts and less coffee.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…Suppose you have preferences for pizza (z) and soda (d). The price of pizza, pz = 5.00 and the price of soda,pd = 2.00. You have an income of I = 20 that you can spend on pizza and soda every week.Suppose you like to always consume 3 pieces of pizzas with 2 cups of soda.•(i) What type of preference do you have for pizzas and sodas?•(ii) Derive the utility function for pizza and sodas•(iii) Solve for your optimal consumption of pizza and sodas•(iv) Illustrate your answer to (iii) on a graph, include your indifference curve, the budget constraint,the slope of the budget constraint, and all labels.