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Price Elasticities and Profit maximization

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1. Answer all the questions in the Memo
Memo 1

To : Pricing Manager, Region 1
From : Regional Manager, Region 1 Cable Systems
Re: Profits from STARZ

We recently added the STARZ Network to our premium cable tier. Currently 852 of our basic service subscribers purchase this service at our current price of $10.50 per month. As, you know, our current contributions from STARZ are not as high as expected. I would like you to evaluate our current price to see if we might be able to raise or lower it to enhance the contributions of STARZ to our revenues.

In an early study of the feasibility of adding STARZ, the marketing department obtained the attached data on the demand and costs for this channel in our Region 1 service area. In addition to the fixed administrative costs, there is a variable cost (license fee) of $5.49 per customer. Please use these data to provide your recommendation about whether we should increase or decrease prices (from $10.50 we are charging now) to increase total profits. I am particularly interested in
1)an estimate of our profit maximization price, and
2)an estimate of how much our monthly profit will increase if we adjust price to your recommended level.

Attachment : Starz.xls

Price Subscribers Other Costs

5 1493 1200
5.5 1500 1200
6 1350 1200
6.5 1224 1200
7 1220 1200
7.5 1210 1200
8 1205 1200
8.5 1212 1200
9 1234 1200
9.5 1104 1200
10 936 1200
10.5 887 1200
11 843 1200
11.5 823 1200
12 750 1200
12.5 648 1200
13 488 1200
13.5 249 1200
14 249 1200
14.5 203 1200
15 178 1200

2. Suppose a firm's demand curve is given by P=120-0.5Q. Find the (value of) price elasticity of demand when the price is $100. Is demand elastic or inelastic.

3.The following is a list of four projects that Capital Corporation must choose from for
the coming year.
Project Project Price Annual Net Inflows
A 700,000 118,861
B 670,000 109,039
C 184,000 32,549
D 273,000 48,305

(a)Given a uniform rate of interest of 9% and a uniform life of the projects of 10 years each. Calculate the NPVs of each project.
(b)Should we choose projects A,C,D or Projects A, B, D. Explain.

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Solution Summary

There are three problems. First problem explains the steps to find out the profit maximization price by developing demand equation by regression. Second solution describes the steps to find out point elasticity of demand. Third solution explains the steps to find NPV of the projects.

Solution Preview

Please refer attached file for better understanding of formulas and tables in MS Excel.

Solution 1 :

Price Subscribers Other Costs Slope Price Elasticity Total Revenue Variable Cost Total Costs Profit 5.49*subscribers Variable Costs+other costs Total Revenue-Total Costs
5 1493 1200 134.1402597 0.449 7465 8196.57 9396.57 -1931.57
5.5 1500 1200 134.1402597 0.492 8250 8235 9435 -1185
6 1350 1200 134.1402597 0.596 8100 7411.5 8611.5 -511.5
6.5 1224 1200 134.1402597 0.712 7956 6719.76 7919.76 36.24
7 1220 1200 134.1402597 0.770 8540 6697.8 7897.8 642.2
7.5 1210 1200 134.1402597 0.831 9075 6642.9 7842.9 1232.1
8 1205 1200 134.1402597 0.891 9640 6615.45 7815.45 1824.55
8.5 1212 1200 134.1402597 0.941 10302 6653.88 ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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