Q1. a) b) c) d) e) f) g) h) There are two goods and John has initial endowment (x1, x₂) (4, 6). Also assume p₁, P2 > 0. Which of the following are definitely true: = = If prices are (p1, p2) = (2, 1) then John can afford the bundle (x1, x2) = (6,5). If John can afford the bundle (x1, x2) = (6,5) then prices are (P₁, P2) (2, 1). = = If prices are (p₁, p2) = (2, 1) then John can afford the bundle (x1, x2) (3,8). = If John can afford the bundle (1, 2) = (3,8) then prices are (p₁, P2) = (2, 1). John can afford the bundle (x1, x2) = (4,4). John can afford the bundle (x1, x2) = (5,5). John can afford the bundle (x1, x2) = (6,6). John cannot afford the bundle (x1, x2) = (5,5).
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- Emma has a utility function U(x1, x2, x3) = log x1 + 0.8 log x2 + 0.72 log x3 over her incomes x1, x2, x3 in the next three years. This is an example of (A) expected value; (B) quasi-hyperbolic utility function; (C) standard discounted utility; (D) none of the above. Emma’s preferences can exhibit which of the following behavioral patterns? (A) preference for flflexibility; (B) context effffects; (C) time inconsistency; (D) intransitivity.Bob has a utility function U(x, y) = √x1 + 0.8√x2 + 0.64√x3 over his incomes x1, x2, x3 in the next three years. This function is an example of (A) expected utility; (B) quasi-hyperbolic utility function; (C) discounted utility; (D) none of the above. . Which of the following preferences agree with Bob’s utility? (A) (9, 10, 11) ≻ (9, 10, 12); (B) (9, 10, 11) ≻ (11, 10, 9);(C) (9, 10, 11) ≻ (9, 11, 10); (D) none of the above. Bob’s utility function implies (A) time stationarity; (B) transitivity; (C) impatience; (D) all of the above.Mats, who has reference-dependent preferences over beer and money, goes to the local pub with a friend, but is not planning on drinking any beer or spending any of his 50 Euro in cash. Let his end-of-evening outcomes in pints of beer consumed and cash be c1 and c2, respectively, and let his reference point in pints of beer and cash be r1 and r2, respectively. Then, Mats’ utility is given by v(6c1 − 6r1) + v(c2 − r2), where v(x) = x for x ≥ 0, and v(x) = 1.5x for x < 0. (a) Suppose that the price of beer is pB. Calculate Mats’ utility from drinking one pint of beer at this price. What is Mats’ utility from drinking no beer? And, comparing these two utility values, what is the maximum price pB that Mats would pay for one beer? (b) Suppose that Mats unexpectedly gets a pint of beer as part of a promotion at the pub, and incorporates its consumption into his reference point in beer. [Hint: this means that (r1, r2) = (1, 50).] Suppose that Mats could sell the beer at a price pS.…
- It is given that a typical consumer has a well-behaved preference structure for his consumption bundle, which includes only two goods, A and B. Further, assume that commodity A is normal and commodity B is Giffen. By keeping commodity A on the x-axis and commodity B on the y-axis, you are required to show the price decomposition for commodity B when $PB decreases exogenously relative to $PA.Student question Time Left :00:09:43Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = 2X + Y UB(X,Y) = Min(X,Y) The initial endowments are: A: X = 5; Y = 3 B: X = 2; Y = 2 a. Illustrate the initial endowments in an Edgeworth Box. Be sure to label the Edgeworth Box carefully and accurately, and make sure the dimensions of the box are correct. Also, draw each consumer’s indifference curve that runs through the initial endowments. Is this initial endowment Pareto Efficient? b. Now suppose Consumer A gets all of both goods. Is this allocation Pareto Efficient? (You do not need to draw a new graph or illustrate this on the existing graph. Simply answer “yes” or “no.”) c. Now suppose Consumer B gets all of both goods. Is this allocation Pareto Efficient? (You do not need to draw a new graph or illustrate this on the existing graph. Simply answer “yes” or “no.”)Suppose Katie buys the bundle (20,9) from the budget line 3x_1 + 5x_2 = 105. When the price of good 1 changes to p1 = 6 and the price of good 2 remains the same, she buys the bundle (5,15). On a later date when p1 = 5 and p2 = 4, by observing Katie’s choices we can say that the Weak Axiom of Revealed Preference (WARP) is violated if a) She buys the bundle (10,15). b) She buys the bundle (15,10) c) She buys the bundle (23,6) d) She buys the bundle (25,25). e) None of the above choices violates WARP.
- Please draw its diagram Consider the following pure exchange economy with two consumers and two goods. Consumer 1 has utility given by U1 = min {4x1, 2x2} Consumer 2 has utility given by U2 = 2x1 + x2 The initial endowment has consumer 1 starting with 200 units of x1 and 200 units of x2. Consumer 2 starts with 300 units of x1 and 300 units of x2. Draw an Edgeworth box diagram for this initial endowment complete with the indifference curves for each individual.Alex preferences over cake, c, and money, m, can be represented by the utility functionu (c, m) = c + m + µ (c − rc) + µ (m − rm)where rc is his cake reference point, rm is his money reference point, and the function µ (·) isdefined as µ (z) = z , z ≥ 0 and λz, z < 0 where λ > 0. 1. If his reference point is the status quo (that is, his initial endowment), what is themaximum price Sam would be willing to pay to buy a cake?2. If his reference point is the status quo, what is the minimum price Sam would be willingto accept to sell a cake he already owned?Consider two treatments. Treatment 1 saves one year of life at a cost of $10,000. Treatment 2 saves ten years of life at a cost of $1,000,000. Which treatment is more cost-effective? Why? Consider two treatments. Treatment 1 saves six years of quality adjusted life at a cost of $90,000. Treatment 2 saves three years of quality adjusted life at a cost of $60,000. Which treatment is preferred from a cost utility analysis perspective? Suppose Jay has been experiencing back pain and that there are two options for back pain: Treatment Regimen Total Cost Pain Reduction Do nothing $0 0 units Cortisone injections $600 30 units Calculate the ICER between cortisone injections and doing nothing. Jay says he is willing to pay $10 for a per unit of pain reduction. Should he choose cortisone injections? Another treatment is discovered. It costs $700 and reduces pain by 25 units. Should he choose the new treatment?
- A consumer who starts (i.e. has an endowment) at point B, and has preferences shown by IC1, will want to borrow. Question 13Select one: True False Question text Assuming a mix of present and future consumption is preferred, ANY consumer who starts (i.e. has an endowment) at point A will gain utility from a rise in interest rates. Question 14Select one: True False Question text A consumer who starts at point B will want to borrow, but as little as possible in order to minimise the cost of interest. Question 15Select one: True False Question text If a consumer starts at point A, and then receives extra income in the present, this would appear as an outward shift of the budget constraint. Question 16Select one: True FalseSuppose that you have two opportunities to invest $1M. The first will increase the amount invested by 50% with a probability of 0.6 or decrease it with a probability of 0.4. The second will increase it by 5% for certain. You wish to split the $1M between the two opportunities. Let x be the amount invested in the first opportunity with (1-x) invested in the second. Find the optimal value of x. Using expected value as the criterion (linear utility) Using the flowing utility function: u(x)=2.3 ln〖(1+4.5x)Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8 logx2+ 0.72 logx3over her incomes x1, x2, x3 in the next three years. This is an example of(A) expected value;(B) quasi-hyperbolic utility function;(C) standard discounted utility;(D) none of the above. Emma’s preferences can exhibit which of the following behavioral patterns?(A) preference for flexibility;(B) context effects;(C) time inconsistency;(D) intransitivity.