2. Assume that a consumer has a budget line l=p1x1+p2x2. Solve for the intercepts [isolate(x1andx2)] of this curve. What is the economic interpretation of these intercepts?
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- Assume that a person's vitility function is given Assume by the following function. TU = 2x¹¹2,¹/2 also that the price of x is 22 and the price of is 26 and that the budget is 2240. what is the optimal amount of goods x and that should be purchused with this budget? of y уEren’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.Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.
- 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. 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).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?
- What is the logarithmic transform of the utility function U=xα1xβ2xγ3 given the budget constraint px1x1+px2x2+px3x3=M . Select one: a. ln U=ln xα1+ln xβ2+ln xγ3 b. ln U=ln xγ1+ln xβ2+ln xα3 c. ln U=α ln x1−β ln x2−γ ln x3 d. ln U=α ln x1+β ln x2+γ ln x3Maria spends all of her income of $2,000 on food (F) and clothing (C). The prices per unit are: PF = $5 and PC = $20. (a) The maximum amount of food that Maria can consume is _____. (b) The maximum number of pieces of clothing that Maria can consume is ____. (c) Therefore the intercepts of Maria’s budget line are _____ F and _____ C. (d) Graph Maria’s budget line, with F on the vertical axis and C on the horizontal axis. (e) Maria (can, cannot) __________ afford to buy a combination of 200 F and 60 C because this combination of goods is located (outside, inside, on) __________ her budget line. (f) The slope of this budget line is _________. (g) The opportunity cost of one piece of clothing is ___ units of food. h) If Maria’s income rises to $3,000, the new intercepts of her budget line are _____ F and _____ C. (i) Graph this new budget line on your graph for item (d) above. Question 2 Use the diagram below to answer the questions that follow. (a) What change could cause the…3- Assuming that the equation F(U, x, X2 = f(x1, x2,, ... Xn): ******* **** ,xn) = 0 implicitly defines a utilityfunction U 073 a) Find the expressions for 60, 6U and 6x4 " 3 6x2 6xn 6x2 6xn b) Interpret their respective economic meanings. c) Now. assume the utility function is U(x, y) = y√x. Does the consumer believe that more is better for each good? Do the consumer's preferences exhibit a diminishing marginal utility of x? Is the marginal utility of y diminishing?
- 5. Consider a consumer that seeks to minimize his expenditure E to achieve a given 1/41/4 level of utilityŪ. Assume that E = p₁x₁ + p₂x²; Ū=x^x^; and p₁ and p₂ are given. a) Set up the Lagrangian. b) Show the first-order conditions or minimization. c) Derive the expressions for the optimal levels of x, and x₂. d) Using the second-order conditions, verify if the solution generates a minimum value for E (Use H₂ to verify).What is the logarithmic transform of the utility function U=xα1xβ2xγ3U=x1αx2βx3γ given the budget constraint px1x1+px2x2+px3x3=Mpx1x1+px2x2+px3x3=M. Select one: a. ln U=ln xα1+ln xβ2+ln xγ3ln U=ln x1α+ln x2β+ln x3γ b. ln U=α ln x1−β ln x2−γ ln x3ln U=α ln x1−β ln x2−γ ln x3 c. ln U=α ln x1+β ln x2+γ ln x3ln U=α ln x1+β ln x2+γ ln x3 d. ln U=ln xγ1+ln xβ2+ln xα3A 2015 report by the music industry estimated the revenue lost to the industry every yearfrom illegal downloading. In this problem we will derive some of the estimates that may havegone into their calculation (approximately).First, start with the individual consumer’s problem. Suppose a typical consumer has a yearlyentertainment budget of I that they can allocate between music downloads (D) and otherforms of entertainment (E). Consumer preferences are characterized by a utility functionU(D, E). a.) Write an expression for the consumer’s budget constraint as a function of their entertainment budget and the prices of music downloads (Pd ) and other entertainment (Pe). (b) Write the consumer’s constrained optimization problem in Lagrangian form. (Note: Youdo not need to solve it or derive first order conditions.)