For the given life time budget constraint; C, + C2 = W1 1 +r determine C1 and C2 to maximize the following utility function 1 C Ut 1- 0 + 1+p1 – 0 1 p = 1 r= 0,5 w = 220 220) ||
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- If a person lives for 3 years with a disease and the current standard of care for that disease means he/she lives with a utility level of 0.7.-What is the QALY? Answer in not less than 300 wordsMaximize Q=K^0.4L0.5 given the equation S+3K+4L=108If 3 mangoes are sold for P^(75), how many mangoes can be bought for P^(150)?
- Exercise 1 A consumer's utility function is u(x, y) = x²y³ and the budget constraint is prx +Pyy ≤ w, where the parameters pr, Py and we are all strictly positive. (a) Solve the consumer's utility maximization problem. (b) Use the envelope theorem to estimate the change in the indirect utility function (i.e., the problem's value function) when the price py is changed to py + e, with e > 0.3. Suppose that the utility functions u(x, y) and v(x, y) are related by v(x, y) = f(u(x, y)). In each case below, check if f is a positive monotonic transformation' of u. (a) f(u) = 3.141592u (b) f(u) = 5000 – 23u (c) f(u) = ! %3D (d) f(u) = -u-1Q6 (a) Mr Jones has utility function U(A,B)= AB. He loses b bananas, reducing his banana holding to B - b. How many extra apples a will he need as compensation, to restore him to his former level of utility?
- For a certain Utility function, which is a simple sifted parabolic equation, the maximum utility is 10 for n=5. Determine the mathematical expression of this Utility function. Hint: look up (h,k) values for a parabola. Multiple Choice 10n + 5 10n + 5n - 2n2 +10n + 5 - (n-5)2+10A consumer is maximising her utility function: U(r. y) = (r05 +y0.5)2, subject to the budget constraint 4x + 2y = 108. (a) Set up the Lagrangian function of this utility maximisation problem and first-order conditions. (b) What are the utility maximizing amounts of x and y? Also, calculate the multiplier. (c) What are the utility maximising amounts of x and y if the budget constrain to x+ 2y = 36? How would change? Explain your reasoning. (Hint: Yc need to calculate A, rather comment on how it would change and why.)6. If intertemporal preferences are consistent and the lifetime utility function is additive, then the discount function 8(t) must be (a) bounded (b) exponential (c) hyperbolic (d) linear (e) logarithmic
- How did you arrive at -0.15 here? MB = (1/3)(90 - 0.6(9,588 + g)½- 0.3g½)To find Susan's optimal contribution, we need to calculate her marginal benefit, which is the derivative of MB with respect to g:MB' = (1/3)(-0.15(9,588 + g)(-1/2) - 0.15g(-1/2))2. Alex and Bill share a flat. Alex enjoys reading in silence, while Bill enjoys listening to loud music. Bill controls his music system, which can produce noise levels up to 100 Decibels. Bill has no cash but Alex has £100. Their utility functions are given by: UA = 10(100 – D)i + (100 – M), %3D Ug = 10(D)i + M, where D denotes the Decibel level chosen by Bill, and M denotes any cash given to Bill by Alex. (a) Explain how Bill's music level affects Alex. Find the contract curve between Alex and Bill. Why is there a unique Pareto efficient noise level? (b) What is the maximum amount Alex would be willing to pay Bill to turn down the music to the Pareto efficient level? What is the minimum amount Bill would be willing to accept in order to turn down the music to the Pareto efficient level? Can the Pareto efficient noise level be achieved through private bargaining?The vending machine in Katherine's office building offers cans of pop and candies. Katherine's utility function is U = 3PC, where P is the amount of pop consumed per %3D week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, she will consume A bags of candy.