You are a pricing analyst for QuantCrunch Corporation, a company that sells a st
ID: 1203025 • Letter: Y
Question
You are a pricing analyst for QuantCrunch Corporation, a company that sells a statistical software package. To date, you only have one client. A recent internal study reveals that this client’s demand for your software is Q=300-0.20P and that it would cost you $1,000 per unit to install and maintain software at this client’s site. The CEO of your company recently asked you compare: 1. The profit that results from charging this client a single per-unit price with (Hint: First find Q* by applying MR=MC, and then find the P*; Find maximum profit using the formula (P*-ATC)Q*) 2. The profit that results from two-part pricing (Hint: set the per-unit price for each unit of the software installed and maintained equal to marginal cost; and charge a fixed “licensing fee” that extracts all consumer surplus from the client) 3. Which pricing strategy would you recommend to your CEO?
Explanation / Answer
Q = 300-0.20P or 0.20P = 300 - Q or P = 1500 - 5Q
TR=P*Q = 1500Q - 5Q^2
MR=dTR/dQ = 1500 - 10Q
MC = 1000
MR=MC for equilibrium
1500 - 10Q = 1000
10Q = 500
Q = 50
P = 1500 - 5*50
P = 1500 - 250 = 1250
Profits = (P*-ATC)Q*)
Profits = (1250 - 1000)*50
= 250*50
= 12500
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