Question 1: Public Good

Sunlight Village is acollege town. There are two student resident units and two facultyresident units. Moonlight Corporationis a monopolist provider of a public botanical gardenin Sunlight Village. Demand (in acres) ofeach student resident unit for the botanical garden isQ = 5 - P, and demand of each faculty resident unit for the garden is Q= 10 - P.Moonlight Corporation faces total cost function of C= 10Q + 2Q² to provide thepublic botanical garden. It is impossible to recognize who is a student resident and who is a faculty resident.

(a)Using the provided space below, draw (i) marginal benefit curve for college student units; (ii) marginal benefit curve for faculty resident units; (iii) marginal benefit curve for total village resident units; (iv) marginal cost curve to Moonlight Corporation;(v) show social optimal level of the garden size. All curves should be clearly labeled and indicate numerical values on both axes.

(b)Sunlight Village citizensworried aboutentrydiscrimination conducted by Moonlight Corporation, so the town assembly imposed the regulation that Moonlight Corporation should sell entry ticketsto all resident units.

(i) How much will Moonlight Corporation charge to each student and faculty resident unit for the garden entry fee?

(ii) What would the profit for Moonlight Corporation be?

(iii) Can this regulation lead to social optimum size of the botanical garden? (Answer Yes or No, and one sentence of explanation is sufficient.)

(c) Suppose thatit is very easy to distinguish between student residents and faculty residents. (e.g. all students have student ID cards with their photos and all faculty members have faculty ID cards with their photos.)

(i) What would the profit for Moonlight Corporation be in this case?

(ii) Is the size of botanical garden under this situation socially optimal? (Answer Yes or No, and one sentence of explanation is sufficient.)

(iii) What is consumer surplus in this case?

Question 2: Weitzman Model

Suppose the benefit from emissions in California is given by , where  is the quantity of emissions  The variable  is unknown to the pollution control board. All they know is that it could take the value of either or , with equal likelihood. Marginal cost of emission is given by .

(a)    What is the marginal benefit of emissions in terms of ?      

(b)    What level of emission fee or emission permit should be chosen, not knowing what value of  will take?

(c)     Suppose that after you have set the fee or permit in part (b), it turns out that Which policy instrument is better without calculation?

(d)   Again,  is known. In a graph where you represent the marginal cost of emissions and the marginal benefit of emission, show the deadweight losses from the permit and the fee. Calculate these deadweight losses (round your answer to the nearest 0.xxx). Does your calculation confirm your answer in part (c)?

Question 3: NPV

Suppose a pharmaceutical firm has a capacity of producing 100 units of a product every year in a competitive market, thus it earns 0 economic profits. Now suppose the firm has an invention that it can patent, and the invention reduces its marginal cost by 5$. In the US, the patentee needs to pay grant fee at the time of grant and 3 renewal fees at year 4, 8, and 12 in order for the patent to stay in life. The schedule of the fees is given in the table below.

For example, after the payment of the grant fee, the patent becomes effective for 4 years; if the renewal fee at year 4 is paid, the patent life is extended for another 4 years; otherwise the patent life elapses. If the all the fees are paid on time, the patent has a full life of 20 years, after which the invention becomes public knowledge such that the firm again earns 0 profits. The profits are collected at the end of each year.Assume the discount rate  (all numbers given in the question are in current terms).

(a)    What is the NPV value of the patent to the firm, if the firm chooses to maintain the patent to its full life. Lay out the steps and show your work. If you don't remember the formulas, you are allowed to use a calculator or spreadsheet.

(b)   Will the firm choose to patent the invention or not? If it chooses to, how long will it maintain the patent? If not, explain.

(c)    As we have learned in lecture, the discount rate depends on many factors. For an invention in a fast moving technology field, you could image the discount rate would be higher. Suppose all the numbers in the question stay the same, except that the firm works in the software industry and has a discount rate of . How does its optimal maintenance of the patent change? You can answer the question by getting the numbers, or you can provide a discussion with good logic.

(d)   (Extra Credit, only if you lose points in the above 3 parts, otherwise no extra credit will be given) Discuss in a few words why you think the patent office has such a monotonically increasing schedule of payments? Remember that the office is a government agency, so think from a social welfare perspective.