Question

The market demand is given as;

P = 100 – Q

Marginal cost of production is given as;

MC = 10

1. Calculate the level at which market decides to produce and market price   
2. Total Revenue ( TR) and Total Cost (TC)
3. Economic Profit (π)
4. Identify the market structure; either perfect competition or monopoly?

Answer 1

The market demand: P = 100 - Q

We know that the market demand curve is also the average revenue of the firm.

Marginal cost = 10

Marginal cost the additional cost incurred for producing an extra unit of product.

a. The profit-maximizing level at which the market decided to produce is at the point where the marginal revenue = marginal cost.

Marginal revenue is the additional revenue generated from an extra unit sold. Numerically, it is the differentiation of total revenue with respect to quantity.

Total revenue = Price*quantity

Total revenue = (100-Q) *Q

= 100Q - Q²

Marginal revenue = dTR/dQ = 100-2Q

At the profit maximizing level of output, MR = MC

100-2Q = 10

Q = 45

This is the profit maximizing level of output. At this output level, price charged will be:

P = 100 - Q

P = 100- 45 = 55

Thus, market output kevel = 45 units and market price = $55

b.

Total revenue = 100Q - Q²

= 100 *(45) - (45)²  

= $2475

Total cost will be the integration of marginal cost functon:

Thus. Total cost = 10Q

Total cost = 10*45 = $450

c.

Economic profit = Total revenue - Total cost

= 2475 - 450

= $2025

d.

This is clearly the case of a monopoly. This is because the demand curve is not perfectly elastic but is downward sloping as can be seen by the equation of the demand curve. Also, in perfect competition, the demand curve = average revenue curve = marginal revenue curve = price of the good (which is constant for all units of output produced).

But here, we can see that the price varies with the level of output produced, as seen by the equation of the demand curve, thus, it is clearly the case of a monopoly.

A monopoly is a type of market structure where there is only one seller of the good in the marker and it has full control over the prices of the goods being sold and thus teh slope of its demand curve is downward.