Economics 331
Fall 2007
Handout #1:Simple Benefit Cost Problems and Constrained Optimization
1.Stephen has a very flexible job. He works everyday but is allowed to take a day off anytime he wants. His friend Dan, suggests they take work off on Thursday and go to the water park. The admission charge for the water park is $15 per person, and it will cost them $5 each for gas and parking. Stephen estimates that a day at the water park is worth $45 to him. However he loves his job so much that he would be willing to pay $10 per day to do it. How much would Stephen have to earn per day for him to be indifferent between going to the amusement park or working.
2.Lindsey has purchased a $40 ticket to a concert. On the day of the concert she is invited to a party for a friend returning from abroad. She cannot attend both events and she does not have to pay to attend the party. If Lindsey had known about the party before buying the concert ticket, she would have chosen the party over the concert.
True or False: It follows, that if she is rational she will go to the party anyway.
3.Residents of Harrisonburg are charged a fixed weekly fee of $6 for trash collection. They are allowed to put out as many bags as they wish each week. The average household disposes of three cans per week. Suppose the city changes to a “sticker” system. Each bag presented for collection must have a sticker affixed to it. The stickers cost $2 each. What prediction do you think the introduction of the sticker system will have on the quantity of trash collected?
4.Allocating Advertising Budget to Maximize Beer Sales
Problem:Suppose you have a $1 million advertising budget that can be allocated between television and radio advertising. The table below shows new beer sales resulting from the different advertising media.
New Beer SalesTotal Spent
(in thousands) / Television / Radio
0 / 0 / 0
100 / 4,750 / 950
200 / 9,000 / 1,800
300 / 12,750 / 2,550
400 / 16,000 / 3,200
500 / 18,750 / 3,750
600 / 21,000 / 4,200
700 / 22,750 / 4,550
800 / 24,000 / 4,800
900 / 24,750 / 4,950
1000 / 25,000 / 5,000
1.Given the information in the table, determine how much money you should allocate to television and radio advertising.
2.Suppose the relationship between the among spend on television and radio advertisement and beer sales can be described as follows:
STV = -0.025BTV 2 + 50BTVSR = -0.005BR 2 + 10BR ,
where S represents sales of beer and B represents the amount of money spent on advertising. How much money should be devoted to each form of advertising now?