The biological relationship between the growth for the fish population and the size of the fish population is g= 12S(1-S/4) where g is the growth of the fish population and S is the size of the population. The size of the harvest is a function of the amount of human effort expended b = 3ES where E is the level of effort. Market price of fish per unit is $100 and a constant marginal cost of effort is $40. The maximum sustainable effort level is an effort level that maximizes b s. Then, the maximum sustainable effort level, Em= integer (you can round the number). Hint: Write an
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- In the Faustmann model, what factors determine the marginal benefits and marginal costs of allowing a stand of trees to continue to grow for another year, and therefore the dynamically efficient harvest interval?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?The number of units Q of a particular commodity that will be produced with K thousand dollars of capital expenditure is modeled by Q(K) = 500 . Suppose that capital expenditure varies with time in such a way that t months from now there will be K(t) thousand dollars of capital expenditure, where K(t) = 2t^4 + 3t + 149 / t + 2 (a) What will be the capital expenditure 3 months from now? How many units will be produced at this time?
- Question #2. Attached (below) is a diagram of a bio-economic model reflecting the relationships between the biological growth of a stock of fish and three different rates of harvest—H1, H2, and H3. In this model, dX/dt=F(X)—the change in the stock with respect to time and biomass— is captured in the parabola. Use the diagram to answer the following questions. On the diagram, the point A refers to a specific and important biological point on the growth curve. What is this point and what is its significance? On the diagram, the point B refers to a biologically important value. What is this value and what is its significance? Consider point C on the diagram. Assume that the stock of fish is just to the right of this point, but still to the left of B. Assume the harvest level is maintained at H3. Over time, what would happen to the stock of fish and the size of the harvest? Consider point D on the diagram. Assume the stock of fish is just to the right of D but still to the left…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.Please answer question 3 a and b b.A clothing manufacturer makes trousers, skirts and blouses. Each trouser requires 20 minutes of cutting time, 60 minutes of sewing time and 5 minutes of packaging time. Each skirt requires 15 minutes of cutting time, 30 minutes of sewing time and 12 minutes of packaging time. Each blouse requires 10 minutes of cutting time, 24 minutes of sewing time and 6 minutes of packaging time. The amount of time available for cutting, sewing and packaging is 115 hours, 280 hours and 65 hours respectively. Using either the Inverse Method or the Cramer’s Rule, determine how many of each type of clothing should be made to use all available labor hours?
- Resource consumption per person in the United States is either flat or falling, depending on the resource. Yet living standards are rising because of technological improvements that allow more output to be produced for every unit of input used in production. What does this say about the likelihood of our running out of resources? Could we possibly maintain or improve our living standards even if the population were expected to rise in the future rather than fall?Resource consumption per person in the United States is either flat or falling, depending on the resource. Yet living standards are rising due to improvements in technology that allow more output to be produced for every unit of input used in production. What does this say about the likelihood of our running out of resources? Could we possibly maintain or improve our living standards even if the population were expected to rise in the future rather than fall?. Find the equilibrium solution of given economic models, a- Qd = 8 – P2 , Qs = P2 – 2
- The productivity of a certain country with the utilization of x units of labor and y units of capital is given approximately by the function f(x,y)=100x0.65y0.35. (A) Find fx(x,y) and fy(x,y). (B) If the country is now using 300 units of labor and 200 units of capital, find the marginal productivity of labor and the marginal productivity of capital. (C) For the greatest increase in the country's productivity, should the government encourage increased use of labor or increased use of capital?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 machinesConsider the following two-period model of dynamically efficient extraction of a non-renewable natural resource. The constant social marginal cost of extraction is 40 in each period and the total stock of the resource is Q = 300 units. Moreover, the social marginal beneÖt is MB(Qt) = 200 Qt, where Qt is the quantity of resource extracted in period t, for t = 0; 1. The discount factor is 0:8.(a) What is the efficient quantity of resources extracted in each period? Provide a graphical representation of the solution. (b) What is the marginal user cost (or scarcity rent) of the resource in each period? (c) Suppose that there is a market to trade the resource. What is the equilibrium price corresponding to each period? Justify the answer. (d) Suppose that it is now expected that because of an extraction technol- ogy improvement, while the Örst period marginal cost of extraction will still remain MXC1 = 40, the second period one will now de- crease to MXC2 = 20. Answer the previous…