Question

1. You have been hired by a new startup. They have been on the market for just a small time and in that time they have offered their product at two prices. They introduced their product at $3.50 and sold 40 units in a month. Then they reduced the price to $3.00 and sold 52 units in a month.

The company has the following costs associated with production: 0.05Q² + 0.90Q. Fixed costs are $20 in rent. The government also charges a tax of $0.10 per unit produced.

a. Given this information, what is the inverse demand function?

b. What is the quantity that maximizes profit? Prove through calculus that it is indeed a maximum.

c. Using Solver in Excel, what is the price that maximizes profit?

d. Calculate the elasticity of demand of the introductory price of $3.50

e. At the introductory price point, what would you predict would happen to both quantity and revue if prices were reduced? Why?

f. At the introductory price point, the company considered increasing price by 2%. What would be the estimated percentage change in quantity?

Answer 1

Notes :

Part c) involves use of an external software hence it's not answered.

therefore, first 4 parts, a, b, d and e have been answered.

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