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- Assume that a country is endowed with 8 units of oil reserve. There is no oil substitute available. How long the oil reserves will last ifa) the marginal willingness to pay for oil in each period is given by P=8-0.57q. (b) the marginal cost of extraction ofol s constant at $4 Per unit and c) discount rate is 1%?A company manufactures Products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for Departments I, II, and III are 1020, 1080, and 900, respectively. The time requirements (in hours per unit) and the profit per unit for each product are as follows. Product A Product B Product C Dept. I 2 1 2 Dept. II 3 1 2 Dept. II 2 2 1 Profit $18 $12 $15 If management decides that the number of units of Product B manufactured must equal or exceed the number of units of products A and C manufactured, how many units of each product should the company produce to maximize its profit?Address the following: a) Suppose that the allocation of a natural resource during three years results in a stream of total surplus value of $100 per period t (i.e.: t = 0; 1; 2). Obtain the present value of this stream when the discount rate is r = 0.10 and also when it is r = 0.05. b) Alternatively, the resource could be fully extracted now (say, in the period t = 0), resulting in a total surplus $280 at t = 0 and 0 in every future period. Is this immediate extraction strategy preferred to the extraction strategy described in (a) when r = 0.10? What about when r = 0.05? What does this tell us about the intuitive meaning of discounting regarding intertemporal preferences c) Explain what it means that a resource allocation is dynamically efficient
- 1. Is scarcity of nonrenewable resources a major problem? What kinds of physical and economic measures are relevant to understanding this issue, and in what ways can some of the measures be misleading? What do you think are the main issues relating to nonrenewable use? 2. Do you expect mineral prices to continue to increase, as shown in Figure 11.4? Which factors do you think will determine future mineral prices?Explain why non-use, or passive use values, cannot be valued either by observing their prices in markets or with revealed preference techniques. Finally, explain how stated preference techniques can be used to estimate non-use value.Assume there are two periods: today (0) and tomorrow (1) and that,after tomorrow the world comes to an end. Further assume there are 10 barrels of oilin the ground. Let the total benefits in each period be given as: B(qt) = 10qt−0.5qt2and the total cost of extracting the oil in each period be 2qt. If the discount rate is10%. Suppose that we use up all the oil in the ground over the two periods.(a) Find the net benefits in each period.(b) If a social planner wants choose a level of output q for periods t = 0and t = 1 so as to maximize the discounted sum of net social benefit over bothtime periods, what is the optimal allocation of output over the two periods?(c) Obtain the prices for the two periods, i.e., p0 and p1.(d) Find the royalty in each period. Show that, the discounted value of the royaltyin each period is the same and it is equal to the shadow price of oil (λ).(e) Verify the Hotelling rule (i.e., show that the growth rate of theroyalty is equal to the discount rate).(f)…
- Suppose we alocate a foxed supply of a depletable resource between two periods in a dynamically efficient way. Assume further that the demand function is constant in the two periods and the marginal willingness to pay is given by the formula P= 7-0.46q while the marginal cost is constant at $1 per unit. The total supply ls 18 units and the discount rate is 2%. What is the marginal user cost during the first period?If consumption is $30,000 when income is $40,000, and consumption increases to $34,000 when income increases to $45,000, the MPC is Select one: O a. None of the options O b. 0.8 O c. 0.2 O d. 0.4There exists 3000 tons of a non-renewable resource (q). Demand is given by P=800−0.25q where P is price. Marginal cost is constant and equal to 200. Assume there are two choices: either to mine the resource today (period 0) or in the next period (period 1). Assume a discount rate of 3%.For each question state: 1.How much will be mined in period 0 and 1, respectively? 2.What is the increase in price in percent between the periods?
- There exists 3000 tons of a non-renewable resource (q). Demand is given by P=800−0.25q where P is price. Marginal cost is constant and equal to 200. Assume there are two choices: either to mine the resource today (period 0) or in the next period (period 1). Assume a discount rate of 3%. a.Assume perfect competition (i.e. P=MR)b.Assume now that MC also increases over time. Say to 300 in period 1. What are the answers then?For each question state: How much will be mined in periods 0 and 1, respectively? What is the increase in price in percent between the periods? c.Again assume constant MC=200. What would happen if there was a monopoly instead?The marginal benefit of being able to emit a ton of sulfur dioxide emissions for two firms are given by:MBX = 1000 – ( Ex / 2 )MBY = 600 – ( Ey / 3 ) Note that these marginal benefit figures can be interpreted as marginal cost of abating emission down to levels Ex and Ey.Government regulators want to reduce total sulfur dioxide emissions to a total of 1800 tons.a) If the government imposes the same standard of 900 tons maximum emissions on both firms what would be the total cost of abatement (calculated as the aggregated marginal benefits forgone)? b) If the government distributed 900 tradable pollution permits (one ton each) to each firm what would be the final allocation of these permits after the firms trade them?c) What would be the total cost of abatement in this latter case?Given - Qd=525−3pQs=265+2pTC=23Q2+150Q A)What is the equilibrium price and quantity? B)What is the new equilibrium price if there is 5 peso tax per unit? C)What is the new equilibrium if there is a 2 peso subsidy per unit? (no tax applied here) D)Solve for Price and Quantity that maximizes profit. What is the max profit? E)What are the break-even quantities?