1. At Lou’s Big City Parking Garage, Lou incurs marginal cost of $1 (MC=$1.00) per
Lou engages in cost-plus pricing (i.e. prices for the long run), AVC is also equal to a
– 0.7Q, where Q is the number of hours of parking per customer, per day, and P is th
Assume, initially, Lou charges a single hourly price.
Use this information to answer the questions below.
NOTE: For some of these questions, you may want to do the work outside of Excel a. With a single price, how much will Lou charge per hour to maximize profit, and how many hours
NOTE: Cost-plus pricing here is consistent with marginal-cost pricing, so follow the MR=MC appro
Hours parked per day,
per customer Profit-maximizing Price
per Hour b. With a single hourly price, what is Lou’s markup and profit margin per customer? (2 pts.) c. With a single hourly price, what is Lou’s profit per customer, per day? (2 pts.)
Note: Enter a formula–using information above–to calculate profit. Suppose Lou is considering an alternative pricing scheme, in which he would charge $6 for the firs
$3 for the next four hours of parking, and $1 per hour for the next three hours of parking (Note: Af
In other words, Lou would engage in block pricing, a form of second-degree price discrimination. d. Under this pricing scheme, and assuming each customer parks for the same number of hours a of $1 (MC=$1.00) per customer per hour. Because MC is constant, average variable cost (AVC
VC is also equal to average total cost (AC). Assume each of Lou’s customers has identical de
, per day, and P is the price of parking per hour. ork outside of Excel and just put your answer in the text box provided. fit, and how many hours will each customer per day? (4 pts.)
follow the MR=MC approach. ustomer? (2 pts.) uld charge $6 for the first three (3) hours of parking,
urs of parking (Note: After 10 hours, Lou would charge a fixed, daily rate).
e price discrimination. ame number of hours as found above (in a.), what would be Lou’s profit per customer, per day? (4 pts.) e variable cost (AVC) is equal to $1, as well, and because
mers has identical demand, given by the expression, P = 8.0 r, per day? (4 pts.) 2. You are a manager in a large hotel chain that is about to open a hotel in a new cit
customers that will stay at this hotel: tourists and business travelers. You can sepa
third-degree price discrimination. To help you determine the profit-maximizing price
50 other cities (these data can be found below). Based on prior research, you know
exponential demand function, of the form: Q = APn, where Q is output (number of ni Part I: For each group of customers, run a regression to estimate "n," the price elas
NOTE: Since this is an exponential function, you will have to first transform the dat
LN(Q) = LN(A) + nLN(P). In this form, the estimated coefficient for the log of P (i.e. "n") will be, in fact, your es
you should obtain a negative value from your regression and not omit the minus sig Part II: Use the results of your regressions to answer the question (determining the
HINT: Look at Slide 10 of the lecture notes.
NOTE: Assume marginal cost for each nightly stay is $50. a. Based on your regression results, enter a formula in the respective boxes below to calculate the
NOTE: Round your answers to the nearest dollar.
Tourists: Business Travelers: DATA: Tourists
Price (per night)
220
202
213
228
225
211
220
198
209
195
203
216
220
212
183
212
220
194
192
230
222
227
207
227
197
183
180
193
223
215
215
211
182
227
196
223
206
205
209
190
224
221
225
208 Nightly Stays per Month
(000s)
80
87
78
70
79
81
76
89
82
86
83
84
73
80
102
83
74
97
88
77
82
79
79
76
87
95
104
90
75
75
75
82
98
72
92
75
81
83
82
92
77
76
73
82 197
180
217
205
201
196 94
105
80
82
82
93 n a hotel in a new city. You have been asked to determine the nightly rates that should be cha
velers. You can separate (and so identify) members of each group based on advanced bookin
ofit-maximizing price for each group, you use a sample of data you have on these same grou
research, you know that demand for both groups exhibit constant elasticity. Therefore, in us
output (number of nightly stays per month), P is price per night, A is a constant, and "n" is th ate "n," the price elasticity of demand for that group. (4 pts.)
rst transform the data into natural logs in order to estimate a linear regression of the form: A) + nLN(P). will be, in fact, your estimate of the price elasticity of demand for that group. ALSO, because "
ot omit the minus sign as you do your calculations. ion (determining the profit-maximizing price for each group). es below to calculate the profit-maximizing price for each group of customers. (6 pts.) Business Travelers
Price (per night)
330
376
349
286
355
303
363
279
276
253
353
369
255
298
363
317
312
345
356
366
372
284
262
341
283
380
315
296
360
275
346
303
370
277
297
265
363
305
276
278
308
349
292
276 Nightly Stays per Month
(000s)
13
11
11
14
9
13
12
16
15
14
11
11
17
15
10
14
11
13
11
9
10
15
17
12
16
11
14
12
10
13
12
13
11
16
13
16
9
13
15
13
12
11
13
13 285
293
261
331
346
296 13
12
15
10
11
13 es that should be charged to the two distinct groups of
on advanced booking. Therefore, you plan to implement
on these same groups of customers for the hotel chain in
city. Therefore, in using the data below, you will assume an
onstant, and "n" is the (constant) price elasticity of demand. ssion of the form: up. ALSO, because "n" is the price elasticity of demand, 3. You have just become the manager of a private golf club, and have been asked to
previously managed public golf courses and know from experience there are two ty
collected (for four years) data on the number of rounds each golfer played that year
at the bottom of this problem, in which you have already divided the data into two e
consisting of 100 "occasional" golfers (those without a subscription). Along with th
round was played. Part I: For each group of 100 golfers, run a regression to estimate a simple demand
explanatory variable) is the price per round, and "a" and "b" are the parameters to b
Part II: Use the results of your regressions to answer the questions below. NOTE: Assume, for all questions, that the club incurs a constant marginal cost (and a. Based on your regression results, write the general expression for the respective demand equa
NOTE: Round the intercept term to the nearest whole number and the coefficient for P to two deci
Serious Golfer Demand: Occasional Golfer
Demand: Serious Golfers Only: Suppose you want to consider what the club’s profit would be
b. How much would the club charge for each round of golf? (2 pts.) c. Enter a formula to calculate the annual membership (entry) fee charged to each golfer. (2 pts.) d. You estimate there are 200 "serious" golfers at your new club. Enter a formula to calculate the
NOTE: For purposes of this question, assume there are no fixed costs. Attracting Both Types of Golfers: Now consider what the club’s profit would be if yo
e. How much would the club charge for each round of golf? (2 pts.)
NOTE: Round answer to the nearest dollar. f. Enter a formula to calculate the annual membership (entry) fee charged to each golfer. (2 pts.) g. You project the club could attract 800 "occasional" golfers, in addition to the 200 "serious" golf
Enter a formula to calculate the club’s profit in this case. (2 pts.)
NOTE: Again, assume there are no fixed costs. DATA:
Serious Golfers
Annual Rounds
(18 holes each) Price
69
68
64
69
65
68
66
70
68
66
69
68
67
67
64
65
68
65
64
65
67
68
66
68
65
64
67
65
67
66
64
66
64 20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00 64
62
65
65
67
67
64
63
63
62
65
62
62
68
64
65
63
62
64
59
60
64
65
64
62
60
62
63
63
63
59
61
63
65
64
64
62
63
62
61
63
59
57
60
61
57
61
63
60 22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00 61
61
61
63
62
61
63
63
63
58
57
63
58
63
62
57
57
58 26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00 d have been asked to come up with an annual membership (entry) fee as well as a price to ch
ence there are two types of golfers: "serious" and "occasional." In fact, you have annual sur
olfer played that year as well as whether the golfer had a subscription to the publication, "Gol
d the data into two equal groups, one consisting of 100 "serious" golfers (those with a subsc
ption). Along with the annual number of rounds for each golfer, you also have the price of a r ate a simple demand equation (i.e. Q = a – bP), where Q (the dependent variable) represents th
e the parameters to be estimated by the regression. ions below. nt marginal cost (and therefore, average variable cost) of $10 for each round of golf. espective demand equation (4 pts.)
fficient for P to two decimal places (e.g. Q = 56 – 1.34P). club’s profit would be if you limited membership to "serious" golfers. to each golfer. (2 pts.) ormula to calculate the club’s profit from limiting membership to just this group of golfers. (2 pts.) profit would be if you priced such that you could attract both "serious" and "occasional" go to each golfer. (2 pts.) o the 200 "serious" golfers who are already members. Occasional Golfers
Annual Rounds
(18 holes each) Price
19
20
20
19
19
20
19
20
20
20
19
20
20
19
19
20
20
19
18
18
19
19
19
18
18
18
18
19
18
19
18
19
19 20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
20.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00
22.00 18
18
18
19
19
19
17
17
18
17
18
18
17
18
17
18
18
17
17
17
18
17
18
18
17
17
17
17
17
18
17
17
17
18
17
17
17
17
17
16
17
16
17
17
16
17
16
16
16 22.00
22.00
22.00
22.00
22.00
22.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
24.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00 16
17
17
17
16
16
16
17
17
16
16
17
16
17
16
17
16
16 26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00 e as well as a price to charge for each round (18 holes) of golf. You have
act, you have annual survey data from your previous job in which you
n to the publication, "Golfer’s Digest." A sample of the data can be found
fers (those with a subscription to "Golfer’s Digest"), and the other group
also have the price of a round of golf corresponding to the year when the nt variable) represents the number of annual rounds of golf, P (the only h round of golf. of golfers. (2 pts.) us" and "occasional" golfers. 4. A company has two divisions. The first produces an operating system for mobile
smartphone. Of course, the company’s smartphone runs on its own operating syst
the operating-system division is $90, while marginal cost in the smartphone division
addition, the price elasticity of demand for this company’s smartphone is a constan
where P is the price per smartphone, and Q is the quantity of smartphones demande
For this entire problem, assume pricing is conducted over the long run (AC = AVC:
In answering the questions below, you will consider two scenarios: Part I: No external market for the operating system (the operating-system chips are Part II: The operating system has its own external market, which is given by the inv
chips (in millions). NOTE: Use marginal-cost pricing (MR=MC) to determine the operating-system divis
cost-plus pricing to determine the price of the company’s smartphone. Part I (No External Market for the Operating System):
a. What is the profit-maximizing price of a smartphone? (2 pts.) b. Enter the formula to calculate the profit-maximizing quantity of smartphones (in millions). (2 pts c. What is the company’s profit (both divisions combined), in millions? (2 pts.) Part II (External Market for the Operating System): a. Calculate the profit-maximizing quantity (in millions) and price of operating-system chips. (4 pts
NOTE: Enter formulas in the respective boxes below. Round both to two decimal places.
Profit-Maximizing
Quantity: Profit-Maximizing Price: b. Enter a formula to calculate the profit (in millions) of the operating-system division. (2 pts.) c. Calculate the profit-maximizing price and quantity (in millions) of the company’s smarthpones.
NOTE: Calculate both to two decimal places.
Profit-Maximizing Price: Profit-Maximizing
Quantity: d. What is the company’s overall profit (both divisions combined)–in millions? (2 pts.) e. Is the company buying or selling operating-system chips on the open market? Briefly explain. ( ng system for mobile devices, such as smartphones. The other division manufacturers and m
s own operating system (NOTE: Each smartphone contains one operating-system chip). Mar
smartphone division–excluding the cost of the chip–is a constant $35 (thus, in this problem,
rtphone is a constant -1.2 at every price level, with demand for the smartphone given by the fu
martphones demanded, in millions. ong run (AC = AVC: all costs are variable). ios: ng-system chips are strictly inputs to the company’s smartphone division). h is given by the inverse demand function: P = 145 – 1.5Q, where P is the price per chip, and erating-system division’s profit-maximizing quantity and price (when there is an external mar
phone. ones (in millions). (2 pts.) ing-system chips. (4 pts.)
decimal places. em division. (2 pts.) mpany’s smarthpones. (4 pts.) ons? (2 pts.) arket? Briefly explain. (2 pts.) manufacturers and markets its own
g-system chip). Marginal cost of a chip in
hus, in this problem,
AVC = MC). In
phone given by the function: Q = 56,375P -1.2., n). e price per chip, and Q is the quantity of re is an external market), but always use
