1. Suppose Frank enjoys traveling and his utility is a function of the number of airplane trips he takes and the number of bus rides he takes. His utility function is given by U(b,p) = 3b0-4p0.8. A trip on a plane costs $400, a trip on the bus costs $50 and Frank has $3,000 to spend on travel. a. Draw Frank's budget line on a graph with bus trips on the vertical axis. b. Calculate AND INTERPRET the slope of Frank's budget line. c. Draw a representative indifference curve on your graph and provide a function that describes the slope of this indifference curve (i.e., find Frank's marginal rate of substitution). What is the INTERPRETATION of the marginal
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- 1. 2. Suppose Frank enjoys traveling and his utility is a function of the number of airplane trips he takes and the number of bus rides he takes. His utility function is given by U(b,p) = 3b0-4p0.8. A trip on a plane costs $400, a trip on the bus costs $50 and Frank has $3,000 to spend on travel. a. Draw Frank's budget line on a graph with bus trips on the vertical axis. b. Calculate AND INTERPRET the slope of Frank's budget line. c. Draw a representative indifference curve on your graph and provide a function that describes the slope of this indifference curve (i.e., find Frank's marginal rate of substitution). What is the INTERPRETATION of the marginal rate of substitution? d. What two conditions must be met in order for Frank to maximize his utility? e. What are the utility maximizing quantities of plane trips and bus trips for Frank? Given income of $1000, Px = 25 and Py = 40, find (1) a function for the MRS and (2) the utility maximizing consumption bundle for each of the…1. Suppose you won $15 on a lotto ticket at the local 7-Eleven and decided to spend all the winnings on candy bars and bags of peanuts. The price of candy bars is $.75 and the price of peanuts is $1.50. a. Construct a table showing the alternative combinations of the two products that are available.b. Plot the data in your table as a “budget” line in a graph. What is the slope of the “budget” line? What is the opportunity cost of one more candy bar? Of one more bag of peanuts?Anatoly's marginal utility for DVDS (D) is MU X and his marginal utility for Xbox games (X) is MUx D. Anatoly's income is $120, the price of a DVD is $20.00, and the price of an Xbox game is $10.00. How many DVDS and Xbox games does Anatoly consume to maximize his satisfaction? Anatoly consumesDVDs andXbox games. (Enter your responses using integers.)
- Kim has $40 per week in her entertainment budget. She splits her time between going to the movies and yoga classes. Each movie costs $10 while each yoga class costs $5. Graph Kim’s budget constraint, with movies on the x-axis and yoga on the y-axis. What is the value of the x-intercept? What is the value of the y-intercept? What is the slope of this budget constraint?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.3. Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony's utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination?
- Write down the equation for the budget constraint and then graph it for .. Px = $100 Py = $25 Income = $5,000.001. An individual's budget Suppose Musashi has a weekly budget of $24 to spend on juice and yogurt. Juice is priced at $2 per gallon, and yogurt is priced at $6 per container. If Musashi spends his entire $24 on juice, he can buy gallons of juice. If he spends his entire $24 on yogurt, he can buy containers of yogurt. Use the blue line (circle symbol) to plot Musashi's budget constraint on the following graph. Next, use the orange point (square symbol) to shade the area that represents combinations of juice and yogurt that are affordable for Musashi. Finally, place the black point (plus symbol) on the point on Musashi's budget constraint that corresponds to a scenario in which Musashi spends $12 on each good. Note: Dashed drop lines will automatically extend to both axes. 24 22 20 BC, ($24) 18 16 Affordable Region 14 12 $12 on Each 6. 4 BC, ($48) 4 6. 8 10 12 14 16 18 24 JUICE (Gallons) 22 20 10 2) YOGURT (Containers)If we have money, we buy goods and services to satisfy our needs. In economics, thesatisfaction that we get from the consumption of goods and services is called utility. Usea utility graph to explain what happen to the utility when you keep on increasing thenumber of units consumed. Also explain what happens to the utility when you keep onincreasing the number of units consumed. Also explain what happens to the additionalutility (i.e. additional satisfaction) when you increase your consumption by one unit
- 1. Muhammad enjoys going to the aquarium (x) and playing basketball (y). His preferences on x and y are described by his utility function: U(x, y) = 100x23y3. He has a budget of £120 per week to spend on playing basketball and going to the acquarium. Knowing that p,=10 and py=10: ,2/3,1/3 (A) Find the optimal combination of x and y so that Muhammad maximizes his utility subject to the budget constraint. Show this graphically. (B) Consider now that the price of going to the aquarium increases to £20, the price of playing basketball is now £15 and the income did not change. How does this modify Muhammad's optimal bundle? Show this graphically. (C) Compare the optima in (A) and (B): has the valuation of y in terms of x changed? Explain.Raymond consumes meatloaves and pineapples. He has decided that hismonthly budget will be $1500. Suppose that one meatloaf costs $375, while one pineapple costs $150. i. Draw a graph of Raymond’s budget line (meatloaf on the y axis). ii. Show how Raymond’s budget line changes if the price of pineapplesincreases to $370.Raymond consumes meatloaves and pineapples. He has decided that hismonthly budget will be $1500. Suppose that one meatloaf costs $375, while one pineapple costs $150. What is the expression for Raymond’s budget constraint? Draw a graph of Raymond’s budget line (meatloaf on the y axis).