EconS 330, Fall 2011 Homework #2: Due on September 28th

Transcription

1 EconS 330, Fall 011 Homework #: Due on September 8th Key Instructor: Ana Espinola, O ce hours: Tuesdays 9:00-10:00, or by appointment 1 Question #1-15 Points You have been assigned to determine the Dynamic E cient allocation of cooper (Depletable resource). Please take into account that the consumption of current generations should not a ect the consumption of future generations. Assume that the inverse demand function for Cooper is P = 110 q and the marginal cost of supplying it is $15 per ton. a. If 85 tons are to be allocated between two periods, in a dynamic e cient allocation how much would be allocated to the rst period and how much to the second period when the interest rate is 15%? (5 Points) b. What would be the e cient price and the marginal user cost MUC in the two periods? (5 Points) c. Identify the net bene ts in both periods and in the case that they are di erent, argue how future generations could be compensated for this di erence. (5 Points) a) q 1 15 = MUC q q 1 + q = 85 First, we need that MUC 1. Hence, using (1) and (3) we have that 110 q 1 15 = 110 q 15 :5 q 1 17:5 = 110 q 15 = 109:5 q 1 = 95 q 14:5 = q 1 q (1) Substituting (3) into (A), Hence, the quantity consumed in period 1 is b) the marginal user cost in period 1 is, and in period, 14:5 = (85 q ) q 14:5 = 97:75 q q q = 83:5 :15 = 38:83 q 1 = 85 38:83 = 4:1 110 q 1 15 = MUC :1 15 = MUC 1 48:83 = MUC 1 1

2 110 q : :84 Price in period 1 p 1 = 110 4:1 = 3:84 p = :83 = 71:17 c) The net bene ts are NB 1 = NB = (110 3:84) 4:1 + (3:84 15) 4:1 = 3; 319:83 (110 71:17) 38:83 + (71:17 15) 38:83 = ; 934:97 The government would like that both generations obtains relatively similar net bene ts. Hence, we can add these two net bene ts and split the result in equal parts (3; 319:83 + ; 934:97 = 54:8 = 37:4). However, current generation is obtaining more than 3; 7:4 (since, 3; 319:83 > 37:4), hence the di erence can be saved for future generations using an interest rate of 15%. That is, 19:43 = 1:9. Hence, NB = ; 934:97 + 1:9 = 315:: Question # - 15 Points Assume the same demand conditions as stated in Problem 1, but let the discount rate be 10%. The marginal cost of extraction in period 1 is $5 and in period is $15 (technological change). How much would be produced in each period in an e cient allocation? What would be the marginal user cost in each period? Would the static and dynamic e ciency criteria yield the same answers for this problem? Why? (15 Points) ) q 1 5 = MUC q q 1 + q = 85 First, we need that MUC 1. Hence, using (1) and (3) we have that 110 q 1 5 = 110 q 15 1 q 1 7:5 = 110 q 15 = 93:5 5q 1 = 95 q 1:5 = q 1 q () Substituting (3) into (A), Hence, the quantity consumed in period 1 is 1:5 = (85 q ) q 1:5 = 93:5 q q q = 95 :10 = 45:4 q 1 = 85 45:4 = 39:7

3 b) the marginal user cost in period 1 is, 110 q 1 5 = MUC :7 5 = MUC 1 45:3 = MUC 1 and in period, 110 q : :3 = MUC 1 Price in period 1 p 1 = :7 = 70:4 p = :4 = 4:7 c) Static versus Dynamic The static analysis will require: D= MC 110 q 1 = 5 q 1 = 85 and given the technological change the quantity in the second period is 110 q = 15 q = 95 The answer is no. The quantities are completely di erent when we use these two distinct concepts. Note that using the static e ciency the resource will be completely exhausted in the rst period since q 1 = 85. However, the Dynamic e ciency provides more egalitarian allocations, since both generations will be consuming similar amounts. In period future generations will be consuming slightly more given the technological change. 3 Question #3-15 Points A rm in a perfect competitive industry has patented a new process for making widgets. The New process lowers the rm s average cost, meaning that this rm alone (although still a price taker) can earn real economics pro ts in the long run. a. If the market price is $0 per widget and the rm s marginal cost is given by MC = 0:4q, where q is the daily widget production for rm, how many widgets will the rm produce? (5 Points) b. Suppose a government study has found that the rm s new process is polluting the air and estimates the social marginal cost of widget production by this rm to be MC S = 0:5q. if the market price is still $0, what is the socially optimal level of production for the rm? What should be the rate of a government-imposed excise tax to bring about this optimal level of production? (5 Points) a) P = 0 and q = 50 b) P = 0, q = 40, MC = 1, and tax = 4 3

4 4 Question #4-10 Points The microeconomic theory of fertility provides an opportunity to determine how public policies that were designed for quite di erent purposes could a ect fertility rates. Europe s working-age population is shrinking as fertility rates decline. In a t of gloom, one German minister recently warned of the country turning the light out if its birth rate did not pick up. E orts to encourage couples to breed have a turbulent history. In Italy for instance Mussolini heavily taxed single men in his Battle for Births and in Germany Hitler awarded medals to women with large families in his quest for a superior German race. Explained how these two policies a ected the Marginal bene t and Marginal Cost of children, and as result the total number of children. Please use a graph to answer this question. First Policy: Mussolini heavily taxed single men; then the cost of an additional child decreases because parents will pay lower taxes. On the other hand, the bene ts of an additional child increase, since a single man will avoid the cost of the tax. Either way the number of child will increase. Second Policy: Hitler awarded medals to women with large families (woman s status increases). This measure will increase the marginal bene t from an additional child and as a result the number of children. Marginal Benefit and Marginal Cost Notice: Q >Q 1 Q 1 Q MB MC 1 MB 1 Quantity of Children 5 Question #5-15 Points Consider an increasing marginal-cost depletable resource with no e ective substitute. a. Describe in general terms how the user cost for this resource in the earlier time periods would depend on whether the demand curve for that resource was stable or shifting outward over time. (10 Points) b. How would the allocation of that resource over time be a ected? (5 Points) Quantity extracted and consumed 8 Marginal Cost 8 Total Marginal Cost Total Marginal Cost a) Notice that the marginal user cost is represented by the distance between the total marginal cost and the marginal extraction cost. Therefore if the demand shifts to the right and the marginal extraction cost (MExC) is increasing, then the resource will be exhausted in earlier periods. In addition, the marginal user cost decreases at a higher rate when the demand shifts to the right. That is, the quantity demanded increases and as a consequence the MExC also increases at each period of time, hence the MUC will decrease faster over time. 4

5 b)the potential reserve (The amount of reserves potentially available depends upon the price people are WTP) would be exhausted in earlier period of time (see graph above). Question # - 10 Points Many states are now imposing severance taxes on resources being extracted in their states. In order to understand the e ect of these on the allocation of the mineral over time, assume a stable demand curve. Use gure 7:5 (chapter 7, 8th and 7th editions) to answer this question a. How would the competitive allocation of an increasing marginal-cost depletable resource be a ected by the imposition of a per-unit tax (for example, $4 per ton) if there exists a constant-marginal-cost substitute? (5 Points) b. Comparing the allocation without a tax to one with a tax, in general terms what are the di erences in cumulative amounts extracted and the price paths? (5 Points) Quantity extracted and consumed Marginal Cost Total Marginal Cost 9 5 Extraction and Consumption of Depletable Resource 4 Consumption of Renewable resource 4 Marginal Extraction cost a)let s assume that the renewable resource marginal cost is constant and it is equal to $. Therefore, if the government imposes a tax of $4 on the extraction of depletable resource, then it implies that the total marginal cost for the depletable resource will increase (as is depicted in the graph). As a consequence, the period of extraction of the depletable resource will decrease (for instance to 4), given that for the society will be cheaper to consume the renewable resource and the transition to the renewable resource would occur sooner. b)allocation with a Tax: the cumulative amount extracted is lower and prices will be higher (they increase at a higher rate than without taxes). Allocation without a Tax: the cumulative amount extracted is higher (it is represented by the area below the blue line until the period, this area is equal to ) and prices will be increasing at a lower rate. 7 Question #7-10 Points What is a public Good? How can one determine the e cient level of a provision of a public Good? (10 points) A public good has two de ning properties: it is no rival and nonexcludable. One way to determine the e cient level of provision is to equate the marginal social bene t of the public good to its marginal social cost. It must be recognized that an additional unit of public good bene ts all consumers at the same time (this is because a public good is nonrival). The marginal social bene t is therefore the sum of marginal private bene ts. The marginal bene t of each consumer can be measured by their marginal rate of substitution between the public good and an alternative private good. 8 Question #8-10 Points A rm can produce steel with or without a lter on its smokestack. If it produces without a lter, the external cost on the community are $500; 000 per year. If it produces with a lter, there are no external costs on the community, and the rm will incur an annual xed cost of $300; 000 for the lter. 5

6 a. Use the Coase Theorem to explain how costless bargaining will lead to a socially e cient outcome, regardless of whether the property rights are owned by the community or the producer. (5 Points) b. How would you answer to part (a) change if the extra yearly xed cost of the lter where $00; 000? (.5 Points) c. Explain the main problems associated with the Coase Theorem. (.5 Points) a) If the rm installs the lter, the community bene ts by $500; 000 while the rms incurs a cost of $300; 000. The socially e cient outcome is for the rm to install the lter. If the rm possesses the right to pollute, the community will have an incentive to pay the rm some price above $300; 000 (Perhaps $499; 999) to induce the rm to install the lter. Afterwards, the community would be $1 better o and the rm would be $199; 999 better o. On the other hand, suppose the community possesses the right to prevent the rm from polluting. The rm then has two choices: it could install the lter at a cost of $300; 000, or it could compensate the community for the cost of its pollution by paying them $500; 001. Since it s clearly cheaper to install the lter, the rm will have a strong incentive to choose this socially e cient outcome. (b) If the lter costs $00; 000, then the socially e cient outcome is for the rm to not install the lter, since the costs exceed the bene ts. If the rm possesses the right to pollute, it will do so. Although the community is willing to pay the rm up to $500; 000 to stop polluting, that does not exceed the rm s costs of installing the lter. If the community possesses the right to prevent the rm from polluting, then the rm will have a strong incentive to compensate the community for the costs of polluting rather than installing the lter. The community could demand that the rm either install the lter or pay it some price less than $00; 000 (say $599; 999). Then the rm would be better o (by $1) installing the lter, while the community also bene ts (by $99; 999) since the payment exceeds the cost of living with pollution. (c) It assumes complete information, transactions cost are zero and it is di cult to coordinate when there are several agents being a ected by an externality.