Question

You are a pricing analyst for QuantCrunch Corporation, a company that recently spent $15,000 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=300-0.2P and that it would cost you $1000 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 $1450 for the first 10 units and $1225 for each recommendation that would result in even higher profits.

Answer 1

Step-by-step explanation:

Base on the scenario been described in the question

First strategy (per-unit price strategy):

According to the given information the demand function is given as:

Economics homework question answer, step 1, image 1

So, the price function can be rewrite as:

Economics homework question answer, step 1, image 2

The firm maximizes the profit at where the marginal revenue (MR) is equal to marginal cost (MC). The MR can be calculated as follows:

Economics homework question answer, step 2, image 1

Since MC is given as 1000, the profit maximization level of quantity can be calculated as follows:

Economics homework question answer, step 3, image 1

Thus, the quantity is 50.

In order to calculate the profit maximizing level of price, substitute the value of Q in price function as follows:

Economics homework question answer, step 3, image 2

Thus, the price is $1250.