You are a pricing analyst for QuantCrunch Corporation, a company that recently s
ID: 1180215 • Letter: Y
Question
You are a pricing analyst for QuantCrunch Corporation, a company that recently spent $10,000 to develop a statistical software package. To date, you only have one client. A recent internal study revealed that this client
You are a pricing analyst for QuantCrunch Corporation, a company that recently spent $10,000 to develop a statistical software package. To date, you only have one client. A recent internal study revealed that this client's demand for your software is Qd = 100 - 0.1P and that it would cost you $500 per unit to install and maintain software at this client's site. The CEO of your company recently asked you to construct a report that compares (1) the profit that results from charging this client a single per-unit price with (2) the profit that results from charging $900 for the first 10 units and $700 for each additional unit of software purchased. Construct this report, including in it a recommendation that would result in even higher profits.Explanation / Answer
profit (pi) = total revenue - total cost
total revenue (TR) = Q^d(P) = (100 - .1P)P = 100P - .1P^2
total cost (TC) = 500(Q^d) = 500(100 -.1P) = 50000 - 50P
marginal revenue (MR) = 100 - .2P
marginal cost (MC) = -50
MC = MR
-50 = 100 - .2P
-150 = -.2P
P = $750
Q^d = 100 - .1P = 100 - .1(750) = 25
pi = P(Q^d) - 500(Q^d)
@ P=$750
pi = (750)(25) - (500)(25) = $6,250
@ P=$900 for first 10 and $700 for each additional unit:
pi = (900)(10) + (700)(15) - (500)(25) = $7,000
Therefore, under the circumstances, charging $900 for the first ten units and $700 thereafter would result in more profit than charging a single per-unit price of $750, which is the profit maximization point for a single per-unit price, however you would need to use Lagrange multipliers in order to maximize profit using a tiered pricing strategy.
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