1. Hot Dogs in Yankee Stadium
There is only one hot dog vendor at Yankee Stadium. The vendor always prices hot dogs in multiples of 25 cents (e.g., $0.50, $2.75, $5.50, etc.) in order for his staff to be able to make exact change easily. During a sold-out Red Sox-Yankees game, the vendor knows from long experience the demand curve for hot dogs, which is given in the table on the right. (Electronic versions of tables are posted on Canvas.)
(a) The vendor's marginal cost of cooking, fixing and providing a hot dog is $1.50. What price should the vendor charge and how many hot dogs would you expect the vendor to sell?
Hot Dog
Stadium
Hot Dog
Price
Sales
$8.00
500
$7.00
2,000
$6.50
4,500
$6.00
7,000
$5.50
9,000
$5.00
12,000
$4.50
15,250
$4.25
17,500
$4.00
20,500
$3.75
23,750
$3.50
27,500
$3.25
32,000
$3.00
36,000
$2.75
41,000
$2.50
45,500
$2.25
51,000
$2.00
57,000
$1.75
62,000
$1.50
67,000
$1.25
69,000
$1.00
71,000
$0.75
74,000
$0.50
77,000
Bleacher Grandstand
Hot Dog
Hot Dog
Hot Dog
Price
Sales
Sales
$8.00
500
$7.00
2,000
$6.50
4,500
$6.00
7,000
$5.50
9,000
$5.00
12,000
$4.50
15,250
$4.25
200
17,300
$4.00
1,000
19,500
$3.75
1,500
22,250
$3.50
2,200
25,500
$3.25
3,000
29,000
$3.00
4,400
31,600
$2.75
6,500
34,500
$2.50
9,000
36,500
$2.25
12,500
38,500
$2.00
14,750
42,250
$1.75
18,000
44,000
$1.50
20,000
47,000
$1.25
21,000
48,000
$1.00
22,000
49,000
$0.75
23,500
50,500
$0.50
25,000
52,000
(b) The vendor notices that one feature of Yankee Stadium is that the bleachers and the grandstand seats have separate entrances, so fans cannot sneak from one section to another. The demand curves for hot dogs in the two sections are given in the table to the left. Should the vendor choose different prices (and sales targets) for each set of spectators? Explain what prices the vendor should set and why.
(c) Just hours before the game, the vendor's main kitchen experiences a major electrical problem, shutting down the majority of its cooking facilities. The unit cost of $1.50 per hot dog remains unchanged, but hot dog production capacity is reduced to only 8,000 units. Suppose that the vendor has the freedom to change prices in light of the production constraint in order to maximize profits from this game's sales and that, as in part (b), the vendor can sell hot dogs for different prices in the bleachers and grandstand. What prices should the vendor set for bleacher and grandstand hotdogs, and how many hot dogs do you expect the vender to sell in each location? Why?
