Question

John is the owner of medium-sized company that assembles personal computers in Ghana. He purchase most of the components for the company such as random access memory (RAM) on a competitive market. In order to maximise profit in the short run, he employed an economist to estimate the demand curve, which he was able to use to derive the marginal revenue (MR) from his product as: ??=70−16?. The economist also derived the marginal cost function (MC) as: ??=6?−51.

(i) Find the total revenue function and deduce the corresponding demand equation.

(ii) Find the total cost function if the fixed cost is 400.

(iii)Determine the number of laptops that maximizes the company’s profit.

(iv)How much should the firm charge for one computer?

(v)Find the total profit at the profit maximizing level of output.

Answer 1

PART A) To find Total Revenue Function, we need to integrate the MR function

Since, Revenue will be earned only when the goods are sold, the value of k in aboive equation is 0

To find Demand Function, we can write the TR function as:

Dividing by Q on both sides

PART B) To find Total Cost Function we need to integrate the MC function

Here, k represents Fixed Cost. We are given Fixed Cost = 400. Hence Total Cost Function is

PART C) Let us define the profit function as:

Differentiating both sides w.r.t Q

Equating it to Zero, we get

PART D) To find the price, put the value of Q in Demand demand function

PART E)

Total Profit at Q* = 5.5, put this in Profit equation