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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 ??
Identify major cross-cultural issues that may impact the American company's marketing approach in this situation and provide a precise description of how the identified issues may impact the approach American company takes.
MacKenzie Company is planning leasing a new asset. The lease would run for eight years and require eight beginning-of-year payments of $100,000 each.
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Using the dynamic augmented Phillip's Curve model (Y/PC/MR), demonstrate the effects of the Following changes. Show both the short-run and long-run effects.
Expected changes in the U.S. real exchange rate vis-a-vis Switzerland and expected rates of inflation in the U.S. and Switzerland.
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Elucidate the price elasticity of supply for your chosen industry.
A Federal Reserve Bank has recruited the economic consulting firm to prepare a paper on how the use of money has changed over the past 20 years.
Suppose capital is steady, with three machines and MPPK/MRCK = 30, determine the least cost input combo of labor and capital? How much output is produced?
Suppose that the Japanese government relaxes its controls on imports by Japanese companies. Other things being equal, how should this affect the.
Elucidate the historical relationship between unemployment and inflation.
A bank loan has a quoted annual rate of 6%. However, the borrower must maintain a balance of 25% of the amount of loan, and the balance does not earn any interest.
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