a) Show that the utility function is strictly increasing in x1 and x2. b) For a given level of utility U, derive the marginal rate of substitution between good 1 and good 2. c) Find the optimal choice of x1 and x2 when the consumer maximizes his/her utility.
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- DmISIIng Margifal Otmty n. TOTAL AND MARGINAL UTILITY Reset E UTILITY CALCULATIONS Total Utility Quantity Consumed Total Marginal Utility 70 Utility 60 50 22 40 1 22 30 18 20 40 10 14 2 3 4 54 Quantity Consumed 10 Marginal Utility 4 64 20 6. 10 70 3. 6. -10 6. 72 -20 -2 7 70 Quantity Consumed Quantity Consumed -6 8. 64 8 Prev 1 of 3 Score answer > ...Please no written by hand and no emage Consider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils.a) Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b) Calculate the optimal weekly consumption bundle for this consumer.c) Does the consumer view C and S as complements or substitutes?Total Total Utility Utility 6 10 10 14 13 15 15 15 16 7 30. If the consumer has only $8 to spend, what would be the optimal consumption of both goods for this consumer? Githe O HD C Number of Colas 1 2 3 4 D 5 a. 4 colas and 2 burgers. b. 5 colas and 1 burger. c. 2 colas and 3 burgers. d. 4 colas and 4 burgers. MUC 6 4 3 2 1 MU/S 6 4 3 2 1 Number of Burgers 1 2 3 4 5 MUb wwwww 10 4 1 0 -8 MU/$ 5 2 0.5 0 -4
- solutions. Question 1 Calculating MRS for CD Utility Functions (a) If a consumer has a CD utility function 0.4 0.6 U(91,92) = 994926, calculate MRS1,2. (b) If a consumer has a CD utility function Ima kdown1 calculate MRS1,2. (c) If a consumer has an utility function noltan asd Tor sympy ,1-α U(91,92) = 91 92 llib et (.) orde (hing aid tol bholup U(91,92) = a ln(91) + (1 - a) ln(92), diw sonuanos of calculate MRS1,2. Is it the same as the result in the previous part? (Note: Recall that we discussed the concept of ordinal utility in class, which means only the order of utility matters, not its magnitude. In function is a monotone transformation on the CD utility function. Notice that In (qq) = a ln(9₁) + (1 - a) ln(92). This example verifies that a monotone transformation does not change *(S) sidshav the consumer's indifference curves.) wobei/ (d)7. Bob receives utility from days spent traveling on vacation domestically (D) and daysspent traveling in a foreign country (F) as given by the utilityU(D; F) = DFThe price of a day spent traveling domestically is 160 pounds and in a foreigncountry 200 pounds. Bobís annual budget for traveling is 8000 pounds. (a) Find Bobís utility maximising choice of days traveling domestically and of daystravelling in a foreign country. Find also his utility level from consuming thatbundle. Suppose that the price of domestic traveling increases to 250 pounds per day.Denoting his budget for traveling x, (suppose by now that it is unknown) findthe demand for D and F under the new prices as a function of x.Is it possible for total utility to increase while marginal utility diminishes? Explain.
- Take Jeremys total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremys utility.Jeremy is deeply in love with Jasmine. Jasmine lives where cell phone coverage is poor, so he can either call her on the land-line phone for five cents per minute or he can drive to see her, at a round—trip cost of 2 in gasoline money. He has a total of 10 per week to spend on staying in touch. To make his preferred choice, Jeremy uses a handy utilimometer that measures his total utility from personal visits and from phone minutes. Using the values in Table 6.6, figure out the points 011 Jeremys consumption choice budget constraint (it may be helpful to do a sketch) and identify his utility-maximizing point.Would you expect total utility to rise or fall with additional consumption of a good? Why?
- Graph the following dataQuantity marginal utility1 153 2 112 3 77 4 48 5 25 6 8 7 -3 8 -8ceriuppose that Isaiah has a weekly fixed budget and spends it all on haircuts and ice cream. At his current combination arof consumption, the marginal utility of the last dollar spent on haircuts is greater than the marginal utility of the last dollar spent on ice cream. Has Isaiah maximized his utility? A C E Yes, because changing his current consumption combination will reduce his total utility B No, because he can increase his total utility by purchasing more haircuts and D fewer ice creams Yes, because he has purchased 2 goods in proportion so that he can get- the maximum utility from each Yes, because he purchased the maximum possible with a limited budget No, because he can increase his total utility by purchasing fewer haircuts and more ice creamsMylie’s total utility from singing the same song over and over is 50 utils after one repetition, 90 utils after two repetitions, 120 utils after three repetitions, 80 utils after four repetitions, 20 utils after five repetitions, and -60 utils after six repetitions, as shown in the table below. a. Write down her marginal utility for each repetition. Instructions: Enter your answers as a whole number. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. Repetitions Total Utility Marginal Utility 0 0 — 1 50 2 90 3 120 4 80 5 20 6 -60