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Investigate the role of ?, the Lagrange multiplier, in constrained optimization problems. Corn is a fertilizer-intensive crop. Agricultural runoff from fields where corn is grown causes eutrophication of rivers, and poisons the nearby ecosystems. Denote corn farmers' use of fertilizer by X. Farmers' profit per acre from the sale of corn is directly related to the amount of fertilizer input they use, and is given by:? = 10 X^(1/2) - XAssume that the cost of damage D to surrounding ecosystems from fertilizer runoff increases quadratically with fertilizer use: D = X^2. In this situation, define social welfare as: W = ? - D.(i) Write down the Lagrangian for this problem, using ? to indicate the Lagrange multiplier. Define what ? is and briefly explain how it applies to this problem.(ii) Suppose that fertilizer use is unregulated. How much fertilizer will farmers use? What will their profit be? How much damage will be caused? What is the net societal benefit?(iii) Now suppose that the local government attempts to limit the environmental damage from runoff to 16 units. How much fertilizer will farmers use now? What will their profit be? What is the net societal benefit? What is the value of ??(iv) In response to pressure from environmentalists the government now tightens the maximum damage standard to 4 units. How much fertilizer will farmers use now? What will their profit be? What is the net societal benefit? What is the value of ??
Illustrate what has been the real change in Bill's net worth.
Choose a social difficulty where free markets are not allowed to function and describe how free market features could be introduced to help alleviate the difficulty.
Pamela Sue, proprietor of Heartland Supermarkets which would like to raise her current sales of corn from 250 bushels per week to 500 bushels per week.
state history of the airline industry, plus an industry overview, and a SWOTT analysis of the airline industry. Please include references.
Discuss the concept of 'instruments and targets' in macroeconomic policy and assess how this concept might be applied to the current policy framework in Australia.
Assume that your firm above is the N.Y. Yankees and the league owners impose a lump sum tax of $4 million dollars on your firm.
Assume that Kiribati can produce 1000 tons of breadfruit or 500 tons of fish, and that Tuvalu can produce 750 tons of breadfruit or 1875 tons of fish.
Show the effect of moving to a consumption tax on the loan able funds market if people react favourably to the incentive to save. Choose which curve or curves you believe are affected.
Prepare a chart that lists three strengths and three weaknesses of the Consumer Price Index calculation.
Suppose Firm Y's production function is given by the following Cobb Douglas equation
This does not required to be loaded with information just basic overview with some graphs, and some notes on the history of Japan's economy and their update.
Suppose demand for the firms watches falls permanently to P = 20 - Q/20,000. In view of this fall in demand, what output should the firm produce in the short run? In the long run? Explain.
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