PROBLEM (5) Cars (x) is a normal good, and public transportation (y) is a substitute for cars. The demand for cars(x) is given by where Qp = 20 ± px ± py ± p{uture ±I where px is the price of cars, Py is the price of public transportation, puture is the expected future price of cars and I is the average income level. (a) Decide whether a plus (+) or a minus (-) sign is appropriate for each “t" in the demand equation above. (b) Does the demand become more or less elastic (at a given px) as py increases? (c) Calculate the cross price elasticity of demand (for cars with respect to the price of public transportation Py) at the point I= 10, Py = 5, py = 2, pfuture = 1
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- Scenario:The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 5kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 5kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnec- essarily paternalistic; depriving low income households of the choice of how to spend their income. These groups argue that the government’s…Scenario The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 10kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnec- essarily paternalistic; depriving low income households of the choice of how to spend their income. These groups argue that the government’s…True/False/Uncertain: 1. In taking an exam, Atack, a rational student, allocates his time to the various questions so as to equalize hismarginal point utility per minute on all questions. 2. The marginal utility of food to Zecher depends only on the amount of food (and not on the amount ofhousing) and the marginal utility declines as more food is consumed; likewise for housing. Therefore,both food and housing are normal goods. (Hint: Express the optimality condition for Zecher’s [UMP], MUF/MUH = PF/PH. Notice that PF/PH is fixed. If all of an increase in income is spent on F, can the equality be maintained?)
- Your own a chocolate producing company which can advertise on both television (T) and internet(I). The effect of TV and online commercials on sales is again given byS(T,I) = 500 + 48T−6T2+ 112I−6I2+ 4TI. You have a budget of $25 that you can spend on T and I. The price of aTV commercial is $12per unit and the price of an online commercial is also $12 per unit. 1. Determine the optimal level of TV commercials T and online commercials I if you have to spend all of your budget. You should provide two methods to solve this, by direct substitution and by setting up the Lagrangian. Is the Lagrange multiplier positive or negative? Give an intuitive interpretation of why this is the case? 2. Now determine the optimal level of TV commercials T and online commercials I if you DO NOT have to spend all of your budget. Do you obtain the same answer as subquestion 5.1? What is the Lagrange multiplier equal to in this case? Discuss.A health club offers two different plans for its visitors. Under plan A, no membership is required and eachvisit costs $10. Under plan B, an annual fee of $200 is paid to become a member and each visit costs only$4. It also sells beverages at a unit price of $10.Let v denote the visits to the health club and b the amount of beverages a customer buys there and pv and pb be their respective prices. Note that pv differs for each plan. Assuming that the potential customers have an annual income of $1000, draw the budget constraints under the two plans on the same graph. [Place v on the horizontal axis and b on the vertical axis.] Label all relevant intercepts and slopes.A small countertop installing company hires you to estimate their customers weekly demand function for marble (per sq ft). The demand function is as follows: Qm=5000-30Pm +20Pg + 0.05Inc m=marble, g= granite, inc = avg disposable income for home improvements in the surrounding area. Current prices: marble = 40, granite = 25 and disposible income = 5000 Suppose during the supply change shortage the price of marble triples to $120 Determine the elasticity of demand at the new market price for marble
- [A] Suppose that a drug company has developed an ointment that can be used to treat sores and reduce scarring. Surveys indicated that the ointment, which costs $10,000 for a full course of treatment, can improve the quality of life from 0.6 to 0.7 for patients with this problem. Assume that this population has a life expectancy of 70 years. No need to worry about discounting. 1. What is the Incremental Cost-Utility Ratio (ICUR) for taking the ointment over doing nothing for a typical 20-year-old patient? [Hint: This patient has only 50 years of life remaining.] 2. If the cost-effectiveness threshold is $5,000 per QALYS, will the 20-year-old patient choose to get the ointment? What about a 60-year-old patient? [B] Is it appropriate to evaluate a healthcare intervention using various methods of economic evaluation as discussed in this course, or should we choose one primary method that best fits the analysis?Q1: The demand for good X is given by Qx d = 6,000 − 1/2 Px − Py + 9 Pz + 1/10 M. Research shows that the prices of related goods are given by Py = $6,500 and Pz = $100, while the average income of individuals consuming this product is M = $80,000. a. How many units of good X will be purchased when Px = $5,230? The calculation should be handwrittena) The demand and supply functions of a particular good are given by the equations 5pq = 10 5p + 5q +15
- The regular air fare between Boston and San Francisco is 419. An airline using planes on this route observes that they fly with an average of 236 passengers. Market research tells the airlines’ managers that each $7 fare reduction would attract, on average, 3 more passengers for each flight. How should they set the fare to maximize their revenue?A printer manufacturer estimates that the average purchaser of a printer will also purchase six ink refills over the lifetime of the printer. The relevant data are: Printer: price: $400, margin: $100 Refills: price: $40, margin: $30 The manufacturer is considering increasing the price of printers by 10% to $440. What volume decrease in the sales of printers is the stay-even sales change for the firm? (Ignore the issue of discounting the value of future ink refill sales. Imagine, for example, that all six are purchased upfront with the printer). A. 11.5% B. 12.5% C. 13.5% D. 14.5% Use = % Q = (Pold - Cold)/(Pnew - Cold) - 1(a) A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good she prefers more to less, with diminishing MRS) chooses optimally to consume 12 units of X. If the prices change and now pX = 6 and pY = 4, what is the possible range for her new optimal X consumption? (b) Forget about (a). A consumer with I=$240 budget is shopping for apples (x) and oranges (y). Apples cost $1 each up until 60 units; thereafter each apple costs $2. Similarly, oranges cost $1 each up until 60 units, and thereafter $2 each. Draw the graph of feasible set of bundles for the consumer with relevant points and numbers (shade the feasible area), no explanation needed. (c)(HARD!) In (b), calculate the optimal bundle assuming the consumer’s utility function is u(x,y) = x5y.