Think the two-period model for a depletable resource such as coal. Period 1 is current time and period 2 is future, a year later. Annual discount rate is 5%. The (inverse) demand function for period 1 is P=27-Q and its marginal (extraction) cost is constant 3. The (inverse) demand function for period 2 is P=15-0.5Q and its marginal (extraction) cost is constant 3. Suppose the supply of coal is limited to 30 units. Marginal net benefit for period 1 is MNB1= Q1. Marginal net benefit for period 2 is MNB2= Q2. Hint: Remember you are not discounting marginal net benefit in period 2 yet.

Think the two-period model for a depletable resource such as coal. Period 1 is current time and period 2 is future, a year later. Annual discount rate is 5%. The (inverse) demand function for period 1 is P=27-Q and its marginal (extraction) cost is constant 3. The (inverse) demand function for period 2 is P=15-0.5Q and its marginal (extraction) cost is constant 3. Suppose the supply of coal is limited to 30 units. Marginal net benefit for period 1 is MNB1= Q1. Marginal net benefit for period 2 is MNB2= Q2. Hint: Remember you are not discounting marginal net benefit in period 2 yet.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter3: Benefits, Costs, And Decisions

Section: Chapter Questions

Problem 2MC

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. Assume the coal resource is in fixed supply and its stock is 15 units of coal. Assume 2 periods of extraction: present and future and a discount rate of r = 10%. The demand function is given by MB = 10 - 0.5q and the supply function is given by a fixed MC cost of extraction MC = $5/unit of coal. a) What is the optimal extraction rate in a static setup of the problem? Show numerically. Why cannot it be applied to this resource? b) What is the optimal extraction rate each period in a dynamic setup of the problem? Show numerically. c) What are the prices and MUC-marginal user costs each period? Show numerically. d) What are the total net benefits obtained if the extraction rate equals the dynamic efficient rate? Show numerically.
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SJ Mask producers would like to seek the advice of your Market Research company to advise and give your analysis of a new mask that allows greater protection from the Covid -19 Virus. The following information about the company was given: The demand equation of x=35000-50p, where x is the demand at $p per mask was given. The cost of producing a mask was at a cost of $20. The company has an ongoing cost of 2000. SJ mask would like to seek advice on a price of $30, if this will be profitable to the company with the hope that it becomes the best-selling mask and production could cease on the other type. Suggestions with reasoning are welcomed on a more appropriate price that would be financially sound. An analysis of the exact and approximate cost of producing 101st mask. An analysis of the cost, revenue and profit function must also be analysed in your advice to the company and the importance in decision making for the marginal functions of each, and what it signifies to the company.…