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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 ??
The Bank of England has switched from interest rate cuts to "quantative easing" This policy involves buying bonds from commerical banks in the hope that these institutions will again lend in vast quantities to businessess and individuals after sit..
Suppose a new deposit to the US banking system of $1000. Assume that all commercial banks have a target reserve ratio of 10 percent and there is no cash drain.
Proponents of trade off liberalization argue which freer trade might actually improve the quality of the environment.
This would obviouslyr equire more pilots, stewardesses, and others that facilitate theair-travel experience. However, suppose at the same time that several of the major airlines experienced a shortage of pilots dueto a strike.
The government finances its purchases through lump-sum taxes on consumers, where T denotes total taxes, and the government budget is balanced every period, so that G = T. The solution for steady state capital per worker k.
Are natural disasters causes of inflation or deflation. Explain where might the public see the evidence.
What is the profit-maximizing output for the monopolist? Calculate its profit.
Assume a country that basically consumes 100 pairs of shoes per hour, all of which are imported. The price of shoes is $40 per pair before a ban on importing them is imposed.
The nation is divided into __12______ Federal Reserve districts, each having a Federal Reserve Bank.
In addition to the shock to the money multiplier as in Question 15, we experience two more shocks that influence the money demand curve: The new, money demand curve is now equal to: Md = 1 X [ 2900 + .5 (5400) - 200 (i)] Explain why we would ex..
The American Nursing Association (ANA) reports that there is a nursing shortage. Develop initiatives to move nurses through graduate studies more rapidly.
Illustrate what are the disadvantages of forming corporate joint ventures between multinational corporations in the home and host country.
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