Using the exponential utility function with α = 0.001, determine which premium is higher: the one for X ∼ N(200,√5000) or the one for y ∼ N(210,√3000) Determine for which values of α the former premium is higher.
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Using the exponential utility function with α = 0.001, determine which premium is higher: the one for X ∼ N(200,√5000) or the one for y ∼ N(210,√3000) Determine for which values of α the former premium is higher.
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- Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person’s utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate δ = 0.05. Hence this person’s goal is to maximize 0ʃ40 e–0.05tu(c(t))dt = 0ʃ40 e–0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = – c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H = e–0.05t(c(t))0.5 + λ(– c(t)) + x(t)(dλ/dt). This person’s wine consumption decreases at a continuous rate of ??? percent per year. The number of bottles being consumed in the 30th year is approximately ???Violet buys pies (x) and champagne (y) with her income of $400 and her utility function over pies (x) and champagne (y) (assumed to be divisible goods, where any real number unit pie or champagne is feasible) is Cobb-Douglas and given by u(x, y) = xy. The price of champagne is pY = $10 per bottle. (a) Pies cost pX = $10 per pie if she buys between zero and 20 pies; if she buys more than 20 pies, each additional pie is half-price, i.e., pX = $5. Draw her budget set, carefully labelling all relevant points. calculate the quantities of pies and champagne she will consume when she maximizes her preferences. (b) (HARDER! We haven’t covered this scenario in class) Pies cost pX = $10 per pie if she buys between zero and 20 pies; if she buys more than 20 pies, each pie purchased is half-price, i.e., pX = $5. The discount applies to all units purchased, not the additional ones! Draw her budget set, carefully labelling all relevant points. Calculate the quantities of pies and champagne she will…Consumer A has a utility function u(x,y) = min{0.5x, 2y) and an income of $250. If the price of x is $10 and the price of y is $5, then the optimal basket (x*y*) is O (10.15, 25.55) O (15.50, 19.0) O (18.44, 13.12) O (22.22, 5.56)
- You have k20 per week to spend and two possible uses for the money: telephoning friends back home and drinking coffee. Each Hour of phoning costs k2 and each cup of coffee costs k1. Your utility function is U(X,Y)=XY,where X is the hours of phoning you do and Y the number of cups of coffee you drink. What are your optimal choices? What is the resulting utility levels? You can use the standard result on the constrained maximization of such a function, but must state in clearlyGiven the following utility functions, check if the utility function is homogeneous and if MRS is diminishing: (1) U(x, y) = Vr + y (2) U(x,y) = (x +y")/5.851Eren’s two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V^2MLast year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV).
- Jerry's utility function is U(x,y) = ( 5x + y ) 18. Find Jerry's MRS (for good X in terms of good Y) and then find the value of the derivative dMRS/dx at the point were x=39 and y=69 and enter it below. Remember to enter the number in decimal form. If the number is negative, then use the negative sign (e.g., -3.29839).Upon graduating from UT this May, you take on a management position working at UtMax theater. You will consider the utility of seeing performance over 1 month, and suppose that at a regular price of $$$ per ticket (my assigned ticket price is 145), customers will see no performance, however with the price reduced by $5, customers will see one performance per month and when reduced by $10, customers will see two performances. As long as the number performances, x, is small, your demand function for performance can be modeled by p=D(x). Write down your demand function.Suppose a consumer lives in two periods , with his income in period 1 as $100 and his income in period 2 as $150. If the rate of interest in the economy is 12%. Find the equilibrium level of consumption in both the periods(C1*,C2*) if his utility function is given as: U = C10.5C20.5. (125 ,125) (138.17, 110.54) (90.54 , 180.84) (110.54 , 138.17)
- Answer the following questions using the following information. Columns 1 and 2 in the table below show the marginal utility that Cody gets by purchasing products A and B. Column 3 shows the marginal utility Cody gets from saving Assume that the price of A is $13 the price of B is $10, and Cody has an income of $129. a) Find the following series of MU/$ for each column. Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places Column 1 Column 2 Column 3 Units of A MU MU/S Units of B MU MU/$ Number of $ saved MU MU/S 68 6.8 1 80 6.15 1. 13 0. 2 71 5.46 2 63 6.3 2 10 0. 3 66 5.08 3 56 5.6 3 7 4 61 4.69 4. 46 46 0. 54 4.15 40 4 45 3.46 31 3.1 6. 1 39 3 22 2.2 0. 29 2.23 8 17 1.7 8 b) What quantities of A and B will Cody purchase in maximizing his utility? Quantity of A: 0 Quantity of B: 0 c) How many dollars will Cody save? Dollars Saved = $0 SAVE AND CLOSEU.S. food markets consumers viewed beef as a normal good from 1960-1976, but viewed it as an inferior good after that point. This type of change is not abnormal, in that as average household incomes rise, preferences might change. For instance, as households move from poor to middle-class, their consumption of beef might increase. However, as households move from middle- class to upper-middle-class, they might choose to purchase more exotic foods products. Assuming you are a beef producer in 1983, what will happen if incomes continue to increase? a. The marginal cost of beef will increase. b. The marginal cost of beef will decrease. c. The demand for beef will increase. d. The demand for beef will decrease.Consider a consumer who can borrow or lend freely at an interest rate of 100% per period of time (think of the period as being, say, 30 years, a bit like with a mortgage). So r = 1.0, or 100%. The consumer's two-period utility function is: U = In(ct) + (1/2)In(Ct+1) The consumer earn Y=100 each period, so Y₁=100 and Yt+1 also equals 100. If this consumer is behaving optimally, trying to maximize her lifetime utility subject to the IBC, what's her consumption in period t?