You are a manager in a large hotel chain that is about

2. You are a manager in a large hotel chain that is about to open a hotel in a new city. You have been asked to determine the nightly rates that should be charged to the two distinct groups
of customers that will stay at this hotel: tourists and business travelers. You can separate (and so identify) members of each group based on advanced booking. Therefore, you plan to
implement third-degree price discrimination. To help you determine the profit-maximizing price for each group, you use a sample of data you have on these same groups customers for
hotels the chain operates in 50 other cities (these data can be found below). Based on prior research, you know that demand for both groups exhibit constant elasticity. Therefore, in
using the data below, you will assume an exponential demand function, of the form: Q = AP n, where Q is output (number of nightly stays per month), P is price (per night), A is a constant,
and "n" is the (constant) price elasticity of demand.
Part I: For each group of customers, run an Excel regression to estimate "n," the price elasticity of demand for that group.
NOTE: Since this is an exponential function, you will have to first transform the data into natural logs in order to estimate a linear regression of the form:
LN(Q) = b1LN(A) + nLN(P).
In this form, the estimated coefficient for the log of P (i.e. "n") will be, in fact, your estimate of the price elasticity of demand for that group. ALSO, because "n" is the price elasticity of
demand, you should obtain a negative value from your regression and not omit the minus sign as you do your calculations.

Part II: Use the results of your regressions to answer the question (determining the profit-maximizing price for each group).

a. Based on your regression results, enter a formula in the respective boxes below to calculate the profit-maximizing price for each group of customers.
NOTE: Assume marginal cost for each nightly stay is $50. Round your answers to the nearest dollar.
Tourists:

Business Travelers:

DATA:
Tourists
Price (per night)
195
208
165
184
192
198
182
193
143
156
194
143
194
163
198
154
210
150
197
195
175
177
159
146
150
207
182
148
144
157
148
194
167
194
185
142
172
140
187
202
209
180

Nightly Stays per Month
(000s)
36
30
51
43
39
37
44
40
58
55
41
59
37
46
40
56
35
51
40
39
40
40
50
60
55
31
42
59
58
53
56
39
47
39
37
56
41
64
41
33
31
44

Business Travelers
Price (per night)
232
222
274
300
263
292
227
294
284
291
296
226
240
259
291
237
243
237
258
293
266
221
254
260
236
239
254
230
260
228
233
298
265
221
298
255
257
237
230
225
279
253

Nightly Stays per Month
(000s)
28
30
21
21
22
19
26
22
23
22
19
27
25
22
22
28
27
27
25
22
22
29
23
24
26
26
23
26
23
27
28
18
22
27
19
25
22
28
27
29
23
26

202
194
149
199
174
206
181
171

32
34
56
34
41
38
44
42

250
249
245
250
229
290
283
285

26
23
26
25
29
20
21
21

3. You have just become the manager of a private golf club, and have been asked to come up with an annual membership (entry) fee as well as a price to charge for each round (18 holes)
of golf. You have previously managed public golf courses and know from experience there are two types of golfers: "serious" and "occasional." In fact, you have annual survey data from
your previous job in which you collected (for four years) data on the number of rounds each golfer played that year as well as whether the golfer had a subscription to the publication,
"Golfer's Digest." A sample of the data can be found at the bottom of this problem, in which you divided it into two groups of golfers: 100 observations of "serious" golfers (those with a
subscription to "Golfer's Digest") and 100 observations of "occasional" golfers (those without a subscription). Along with the annual number of rounds for each golfer, you also have the
price of a round of golf corresponding to the year when the round was played.
Part I: For each group of 100 golfers, run an Excel regression to estimate a simple demand equation (i.e. Q = a - bP), where Q represents the number of rounds of golf , P is the price per
round, and "a" and "b" are the parameters to be estimated by the regression.
Part II: Use the results of your regressions to answer the questions below.
NOTE: Assume, for all questions, that the club incurs a marginal cost of $10 for each round of golf.

a. Based on your regression results, write the general expression for the respective demand equation
NOTE: Round constant term to nearest whole number and slope coefficient to two decimal places (e.g. Q = 56 - 1.34P).
Serious Golfer Demand:

Occasional Golfer
Demand:

Serious Golfers Only: Suppose you want to consider what the club's profit would be if you limited membership to "serious" golfers.
b. How much would the club charge for each round of golf?

c. Enter a formula to calculate the annual membership (entry) fee charged to each golfer.

d. Based on just the number of golfers in this sample of data, enter a formula to calculate the club's profit?
NOTE: For purposes of this question, assume there are no fixed costs.

Both Types of Golfers: Now consider what the club's profit would be if you priced such that you could attract both groups of golfers.
e. How much would the club charge for each round of golf?
NOTE: Round answer to the nearest dollar.

f. Enter a formula to calculate the annual membership (entry) fee charged to each golfer.

g. Based on just the number of golfers in this sample of data, enter a formula to calculate the club's profit?
NOTE: Again, assume there are no fixed costs.

DATA:
Serious Golfers

Occasional Golfers

Annual Rounds
(18 holes)

Annual Rounds
(18 holes)

Price
59
57
54
59
58
54
57
59
60
56
58
58
54
56
57
60
55
57
58
58
54
56
56
51
51
51
57
52
51
55
57
57
55
54
56
55
58
51
52
56
57
58
53
53
57
56
54
58
58
53
55
53
50
52
49
51
55
50
51
51
49
53
55
51
51
51
53
48
50
54
51
51
48

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
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

Price
21
21
20
23
23
23
22
20
22
20
21
22
22
22
21
22
20
22
19
22
21
21
22
20
19
22
20
22
20
19
22
21
21
22
19
19
20
20
22
20
18
18
21
21
20
21
20
21
18
21
19
21
19
19
18
20
21
20
18
20
21
21
21
20
21
20
20
21
19
20
20
18
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
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

46
47
48
48
47
47
50
47
52
51
45
50
45
51
52
48
45
46
46
47
51
47
51
48
51
45
50

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
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00

17
20
20
20
20
19
17
20
18
18
20
19
19
20
19
17
17
17
17
20
17
19
18
18
19
20
19

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
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00
26.00

4. An aerospace company has two divisions. The first division makes rockets, purchased by both the government and private firms. The other division makes the engines used by those
rockets. (NOTE: Each rocket requires one engine). Marginal cost in the engine division is a constant $7.92 million, while marginal cost in the rocket division--excluding the cost of the
engine--is a constant $16 million (thus, in this problem, AVC = MC). In addition, the price elasticity of demand for rockets (by all purchasers) is a constant -1.62 at every price level, with
demand for rockets given by the function: Q = 36,520P --1.62.
For this entire problem, assume pricing is conducted over the long run (AC = AVC: all costs are variable).
In answering the questions below, you will consider two scenarios:
Part I: No external market for engines (they are strictly inputs to the company's rocket division).
Part II: Engines have their own external market, which is given by the inverse demand function: P = 22 - 0.15Q, where P is the price (in millions) and Q is the quantity of engines.
NOTE: Use marginal-cost pricing (MR=MC) to determine the engine division's profit-maximizing quantity and price (when there is an external market), but always use cost-plus pricing to
determine the price of a rocket.

Part I (No External Market for Engines):
a. What is the profit-maximizing price of a rocket (in millions of dollars)?
NOTE: Round your answer to two decimal places.

b. Enter the formula to calculate the profit-maximizing quantity of rockets.

c. What is the company's profit (rocket and engine divisions combined), in millions?

Part II (External Market for Engines Exists):
a. What is the profit-maximizing quantity and price (in millions) of engines?
NOTE: Enter formulas in the respective boxes below. Round both to nearest whole number.
Equilibrium Quantity:

Equilibrium Price:

b. Enter a formula to calculate the profit (in millions) of the engine division.

c. Calculate the profit-maximizing price and quantity of rockets.
NOTE: Round both to nearest whole number.
Equilibrium Price:

Equilibrium Quantity:

d. What is the company's overall profit (both divisions combined)--in millions?

e. Is the company buying or selling engines on the open market? Briefly explain.