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Q1: Imagine that 20 units are to be allocated between two periods. Let the inverse demand...
Maximization of net benefits for a two period model (also profit maximization of a single owner)....
Maximization of net benefits for a two period model (also profit maximization of a single owner). Two conditions must be satisfied: (P2 – MC2) = (1 + r)(P1 – MC1) q1 + q2 = qtotal In the numerical example given in lecture, the inverse demand function for the depletable resource is P = 8 – 0.4q and the marginal cost of supplying it is $2. If 20 units are to be allocated between two periods, in a dynamic efficient allocation...
Please answer all of the following Question 4. Non-Renewable Resource: Two Period Model (30 points) Consider...
Please answer all of the following
Question 4. Non-Renewable Resource: Two Period Model (30 points) Consider the following two-period model of a depletable resource: 1. The demand for the resource in period 1 is MB. = 30 - Q.; 2. The demand for the resource in period 2 is MB2 = 40 - Q.; 3. The marginal extraction costs is MC = 10 in each period; 4. The discount rate is 50% (r = 0.50); 5. The total known stock...
1. Consider a two-period model similar to the one discussed in the class. Assume that the...
1. Consider a two-period model similar to the one discussed in the class. Assume that the inverse demand equations for a particular depletable resource (e.g., stock of oil) differs across the two periods, with MB. = 600 - 90 MB = 800 - 91 Where, 9. denotes the amount of oil consumed in period 0 and q, denotes the amount consumed in period 1. The higher demand for oil in period 1 might result, for example, from an increased population....
Assume we have a fixed supply of a depletable resource to allocate between two periods. Also...
Assume we have a fixed supply of a depletable resource to allocate between two periods. Also assume that the demand function is the same in each of the two periods, given by the formula P = 4 – 0.2q, and the marginal cost of supplying the resource is constant at $1 per unit. Now, assume the available supply of the resource q is 10 units, and the discount rate is 10%. What is the dynamically efficient allocation of this resource?...
4. (28 points) The inverse demand for a scarce depletable resource, same function for every period,...
4. (28 points) The inverse demand for a scarce depletable resource, same function for every period, is given by P = 20 – 0.29e, where t = 0,1 denotes the time. Period t = 0 is now and period t = 1 is the next period. The marginal cost of extraction, same function for every period, is given by MC = 2+0.196. (a) Assume that the available stock of this depletable resource is = 40 units and the discount rate...
Suppose coal is only to be extracted over two periods. The inverse demand for coal is...
Suppose coal is only to be extracted over two periods. The inverse demand for coal is estimated to be P = 300 - 2Q, where P is the price of coal and Q is the quantity demanded. The marginal cost of extraction is given by MC = 2Q. These relations do not change from period to period. Assume discount rate r = 0.05. Also assume the total initial stock of coal is S0 = 100 for all parts of this...
A nonrenewable resource stock of 200 units Two periods Demand in the first period (period 0)...
A nonrenewable resource stock of 200 units Two periods Demand in the first period (period 0) is p 0 =300-q 0 Demand in the second period (period 1) is p 1 =400-2q The marginal extraction cost is zero. Competitive industry, profit maximizing firms 1 a. Draw the 2-period graph for this case. On your graph, label the values of all vertical intercepts for the two demand curves (1 pt.) b. State the value of the quantity that would be extracted...
4. Suppose that South Africa is trying to find the efficient amount of coal to extract,...
4. Suppose that South Africa is trying to find the efficient amount of coal to extract, which is a depletable resource. There are two periods and the inverse demand function is P = 15 - 0.5QD and the marginal cost of extraction is 5. (a.) Use the static efficiency model to find the efficient allocation for the first time period. Also, compute the price of coal at that efficient allocation. (b.) Now suppose that the total available quantity of coal...
Suppose that we need to develop a model to help us to allocate a resource between...
Suppose that we need to develop a model to help us to allocate a resource between two time periods: Period 1 and Period 2. Demand can be characterized in both periods as: P = 20 – 2Q. In both periods the marginal cost of extracting the resource is constant at $4 per unit. The total quantity of the resource that is available to allocate between the two periods is 18 units (in other words, Q1 + Q2 <= 18). Assume...
1. Assume the following two equations and the discount rate for the extraction of a natural...
1. Assume the following two equations and the discount rate for the extraction of a natural resource: A) P= 18 -0.75 Q for Marginal Willingness to Pay B) P= 3 for a constant Marginal Cost C) Discount Rate = 6% Solve for the following in a two time period setting: 1) Find and label the equilibrium when there is no limit on Q. 2) State the assumptions needed to solve the optimal extraction rate of the resource in our setting....
Please answer all of the following
Question 4. Non-Renewable Resource: Two Period Model (30 points) Consider the following two-period model of a depletable resource: 1. The demand for the resource in period 1 is MB. = 30 - Q.; 2. The demand for the resource in period 2 is MB2 = 40 - Q.; 3. The marginal extraction costs is MC = 10 in each period; 4. The discount rate is 50% (r = 0.50); 5. The total known stock...
1. Consider a two-period model similar to the one discussed in the class. Assume that the inverse demand equations for a particular depletable resource (e.g., stock of oil) differs across the two periods, with MB. = 600 - 90 MB = 800 - 91 Where, 9. denotes the amount of oil consumed in period 0 and q, denotes the amount consumed in period 1. The higher demand for oil in period 1 might result, for example, from an increased population....
4. (28 points) The inverse demand for a scarce depletable resource, same function for every period, is given by P = 20 – 0.29e, where t = 0,1 denotes the time. Period t = 0 is now and period t = 1 is the next period. The marginal cost of extraction, same function for every period, is given by MC = 2+0.196. (a) Assume that the available stock of this depletable resource is = 40 units and the discount rate...
1. Assume the following two equations and the discount rate for the extraction of a natural resource: A) P= 18 -0.75 Q for Marginal Willingness to Pay B) P= 3 for a constant Marginal Cost C) Discount Rate = 6% Solve for the following in a two time period setting: 1) Find and label the equilibrium when there is no limit on Q. 2) State the assumptions needed to solve the optimal extraction rate of the resource in our setting....
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