Suppose that the marginal cost of extracting a non-renewable natural resource is MXC(Q) = 10 and the marginal beneÖt of using the resource are MB(Q) = 90Q. In the context of a static model, address the following question: Calculate the efficient value of Q if the total stock of the natural resource is Q = 50: Provide a graphical representation of the solution.
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Suppose that the marginal cost of extracting a non-renewable natural resource is MXC(Q) = 10 and the marginal beneÖt of using the resource are MB(Q) = 90Q. In the context of a static model, address the following question:
Calculate the efficient value of Q if the total stock of the natural resource is Q = 50: Provide a graphical representation of the solution.
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- The demand and supply of pizza is defined by the following equations: Qd = D(P, Y ) = 1 + Y − 2P Qs = D(P, PM) = 2 P/PM where, Qd is quantity demand, P is the price of each pizza sold, Y is the average income of consumers, Qs is the quantity supplied, and Pm is the price of inputs used in the production of pizza. (a) List the endogenous and exogenous variables of this model (b) Find the equilibrium price Pe and quantity Qe of pizza as a function of the exogenous variables. (c) Use a simple demand and supply diagram to show what happens to the equilibrium price and quantity when there is an increase in one of the exogenous variables.Assume you own a copper mine. The mine has total known reserves of 500 (million metric tons). The market demand for the copper is estimated to be: P = -1.75Q + 1000 and the marginal cost curve is estimated to be: P = 1.25Q + 100. What is the efficient quantity of copper to extract if you need only consider the current period in your decision making? Assume you need to consider allocation of the mine’s resources across two periods of time—the present and the future. Assume the “future” period is 10 years from the present and you use a discount rate 7.5%. What would be the efficient (inter-temporal) allocation of the mine’s resources in each period? What would be the price in each period if demand is constant across time?Problem 3: The following is an excerpt from an article published on October 9, 2015by the Wall Street Journal (the whole article is available as a separate document under the assignment folder): The U.S. Department of Agriculture, in a monthly report Friday, pegged corn output this autumn at 13.555 billion bushels on yields of 168 bushels an acre, topping analyst estimates for 13.461 billion bushels on yields of 166.4 bushels an acre. The government's yield forecast would mark the second highest behind last year's record 171 bushels per acre. Analysts expected the USDA to trim its yield forecast because of rainy weather early in the growing season in the eastern Midwest, which drew off nutrients from the soil and impeded some plant growth. But the government projected huge yields in the western Midwest, including Iowa, Minnesota and Nebraska. If there is one thing the report showed, it is "there's no shortage of grain in the U.S. or the world," said Don Roose, president of U.S.…
- A clothing company can use one of the following four production processes to produce 5,000 garments per month. Which production process is the most productively efficient? One that involves 20 workers and 20 machines One that involves 30 workers and 50 machines One that involves 30 workers and 20 machines One that involves 20 workers and 50 machinesSuppose the relationship between your study time and your grade on a History midterm is given by the following table: If you study for Your grade will be 4 hours 80 5 hours 90 6 hours 93 a) What is the "marginal grade improvement (MGI)" of the 5th hour of studying? b) What is the "marginal grade improvement (MGI)" of the 6th hour of studying? c) Why might the MGI be diminishing?The production of a product is characterised by the function f(x, y) = 16x/4y3/4, where x is the number of units of labour and y is the number of units of capital needed to produce f(x, y) units of the product. Each unit of labour costs £50 and each unit of capital costs £100. You are given a budget of £500,000 and are asked to calculate the number of units of labour that maximise the production. Enter your answer as an integer. Answer:
- Let H = G - G be the amount that gunk, G, is reduced from the %3D competitive level, G. The benefit of reducing gunk is B(H) = AH*. The cost is C(H) = HP . If the benefit is increasing but at a diminishing rate as H increases, and the cost is rising at an increasing rate, what are the possible ranges of values for A, x, and B?Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function. S = 20L0.30C0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 40,000 tons of steel at minimum cost. Min s.t. = 40,000 L, C 2 0 (b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L > 0 and C > 0. Round your answers to the nearest integer.) $ at (L, C) =Assume the relationship between the growth of a fish population and the population size can be represented as g= 8S – 0.2S2, where g is the growth in tons and S is the size of the population (in thousands of tons) a. Given a price of $100 a ton of fish, what is the marginal benefit of smaller population sizes?
- Green et al. (2005) estmate the supply and demand curves for Californa processod tomatoes. The supply function is: \[ \ln \left(Q_{s}\right)=0.200+0.550 \ln (p) \] whereQis the quantify of processing tomatoes in milions of tons per year andpis the price in dollars per ton. The demand function is: \[ \ln \left(Q_{d}\right)=2600-0.200 \ln (p)+0.150 \ln \left(p_{1}\right) . \] wherep1is the price of tornato paste (which is what processing tomatoes are used to produce) in dollars per ton. Supposept=$119Determine how the equilerium price and quantity of processing tomatees change if the price of tomato pasise tails by16%. If the price of tomato paste fals by18%, then the equaborium price will by 5 (Enter a numene response using a real number rounded to two decimal places)The cost of controlling carbon dioxide emissions [C(E)] at a firm goes up rapidly as the amount of emissions (E) increase. Let's assume the relationship is defined by the function below. C(E)= 5000+ 40E +2E² E20 where E is measured in tonnes per year and C is measured in dollars per year. a) Determine the Marginal Cost function for controlling carbon dioxide emissions and find the marginal cost at 50 tonnes of emissions: b) Determine the Average Cost Function for controlling carbon dioxide emissions and find the tonnes of emissions at minimum average cost. c) The government is charging a tax of $270 for every tonne of carbon dioxide emitted. At, 50 tonnes of emissions, is it profitable for the firm to control emissions on its own or pay the carbon tax?For firm A, is the following an internal or external economy of scale? Firm A benefits from a pool of trained labour in the area.