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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 ??
Is the equilibrium real output also necessarily the full-employment real output and Sketch in the new aggregate demand curve as AD. What is the new equilibrium price level and level of real output?
Determine what effect on a country's current account balance is an increase in use of quotas expected to have? Would your answer change if other governments retaliate? If so, how?
Assume an airline flying on the Charlotile - Chicago route has estimated the demand curves for three different types of customers: business
The TiVo video recorder, the iPod music player and the Xbox game machine all owe their existence to the same high-tech innovation: smaller, denser, cheaper disk drives.
Explain the level of resource misallocation comparing the outcome under the Monopoly situation with the outcome under perfect competition
GDP per capita in a nation like Switzerland can have a low GDP per capita also still have a high standard of living.
Given the table of marginal utilities for CD's and century books, calculate the optimal quantity and total utility at equilibrium. Draw Sarah's budget line for part a and her budget line for part b on the same graph.
They could have rented it on the open marketplace for $700 per month. The condo owner was formerly renting the unit for $500 every month.
In perfectly competitive market a company typically has short run average total cost curve and marginal cost curve of;
Assume Madison has sixteen hours in the day for work or leisure. She earns $5 an hour and receives $15 each day in non-labor income.
Do the estimated coefficients have the required signs to yield a-shaped AVC curve? Discuss the significance using the p-values.
Provide reasons why monopolists do not exhibit resource allocative efficiency. Why monopolists cannot obtain any price they wish.
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