What is the objective function for the problem

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Reference no: EM131225211

PROBLEM SET ONE FALL 2016

1. Consider the attached article from the Wall Street Journal.
https://www.wsj.com/articles/the-thorny-economics-of-illegal-immigration-1454984443

It is a great application of the net-benefit calculus in action.

a. Decide what the appropriate variable will be on the horizontal axis of the net-benefit calculus analysis. Carefully define the benefits and costs within the context of this article.Defining the variable on the horizontal axis is a critical step as it determines how you classify benefits and costs.

b. Illustrate graphically using MB-MC analysis (no total analysis) how Arizona's anti-immigration laws will promote or deter the maximization of net-benefits. Provide a before and after analysis (i.e. before the anti-immigration laws were passed and after). Explain both cases.

c. Employers of illegal immigrants claim they are having a difficult time filling jobs. They contend that the benefits from illegal immigrants are significantly understated. How would the understatement of benefits affect your analysis in part b? Illustrate and explain highlighting relevant areas. Be sure to label and refer to the gains and losses and change in net-benefit with the understanding that the true benefits of illegal immigration are understated.

2. A major automobile manufacturer is considering how to allocate a $2 million advertising budget between two types of television programs: NFL football games and PGA tour professional golf tournaments. The following table shows the new sports vehicles (SUVs) that are sold when a given amount of money is spent on advertising during a NFL football game and a PGA tour golf event.

Total Spent (millions) New SUV Sales Generated (thousands of vehicle per year)
                                           NFL FOOTBALL               PGA GOLF TOUR
$0                                             0                                    0
$0.5                                          10                                  4
$1.0                                          15                                  6
$1.5                                          19                                  8
$2.0                                          20                                  9

a. What is the objective function for this problem?

b. What is the constraint?

c. What are the exogenous and endogenous variables?

d. What is the solution to this constrained optimization problem? Explain beyond a shadow of a doubt why this is the best expenditure of your advertising budget.

3. In Providence, price elastic of demand in absolute terms is 0.6, the income elasticity of demand for bus rides is -0.16 and the cross price elasticity of demand for bus rides with respect to gasoline is 0.25. The price of a bus ride is $3.00. At that price, the daily demand for bus rides in the city is 1000 riders.

a. Begin by deriving the equation for the demand curve mathematically. Show all of the steps used to derive the demand equation. Based on this equation, graphically illustrate labeling intercepts and initial price and quantity.

b. If the average income in Providence increases from $25,000 to $30,000, with no change in the price of a bus ride, how will the number of riders change? Illustrate graphically using the same graph from part a. Provide specific numbers. Show all calculations.

c. After the income increased (start where you left off in part b), the price of gasoline decreases from $3.00/gallon to $2.50/gallon, with no change in the price of a bus ride, how will the number of riders change? Illustrate graphically and provide specific numbers.

d. Assume the supply function has been estimated to be Qs=167P. Draw the corresponding supply curve. What will be the final equilibrium price and quantity? Label your graph accordingly.

4. The demand and supply curves for pizza have been estimated at follows:

Qd= 700-20P-5Y and Qs=360+ 10P-20Pc

Where Y=Income=$20,000, Pc=price of chesse=$3.00/lb, P=price of pizza. Qd and Qs are measured in thousands.

a. What is the equilibrium price and quantity of pizza? Illustrate this equilibrium graphically. What is so special about equilibrium?

b. The price of cheese has fallen to $2.00/pound. What will be the new equilibrium price and quantity of pizza? Illustrate graphically using the same diagram from part a. Clearly explain the transitional process that takes you from one equilibrium to another. Be sure to use arrows and explain them when describing the transitional process.

c. What would happen to this equilibrium position if income falls to $15,000? Using the same diagram, show the new equilibrium price and quantity that results from this change. No transitional process necessary.

d. Can we always say with certainty what the final impact on the equilibrium price and quantity of pizza will be? What does it depend on? Explain using the shifts that occurred in this problem.

e. Calculate the price elasticity of demand for pizza. Interpret the value of the coefficient.

Reference no: EM131225211

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