# The inverse demand function for a monopoly is p = 350 - 3.5Q. a) What is its marginal revenue...

## Question:

The inverse demand function for a monopoly is p = 350 - 3.5Q.

a) What is its marginal revenue function?

b) Draw the demand and marginal revenue curves. Label the quantities where the demand and marginal revenue hit the quantity axis.

## Introduction to Monopoly:

Monopoly is a market which has only one seller. Thus, the firm is inseparable from the industry. This is because the commodity is one of it's kind and has no close or perfect substitute. The monopolist is a price maker(This means that the monopolist will determine the price that has to be charged). Due to inelastic demand for this product, the consumer will be willing to pay any price that the producer charges(the demand is inelastic because there is no substitute). Another important feature of monopoly is price discrimination. Here the producer charges different prices to the consumers based on the type of consumers, type of goods and the geographical area where the commodity is sold.

## Answer and Explanation: 1

a) The price is nothing but average revenue (AR) of the firm.

We know that

{eq}AR= 350 - 3.5Q. {/eq}

Hence the Total Revenue(TR) is given by

{eq}AR \cdot Q {/eq}

Where Q is the quantity

{eq}TR= 350Q - 3.5Q^2. {/eq}

{eq}MR = TC' {/eq}

therefore the equation for MR will be

{eq}MR= (350Q - 3.5Q^2)' {/eq}

{eq}MR= 350 - 7Q. {/eq}

b) We know that the inverse demand function is given by

{eq}p= 350 - 3.5Q. {/eq}

Therefore when the demand function will touch the Quantity axis, price will be zero

{eq}0= 350 - 3.5Q. {/eq}

{eq}350 = 3.5Q. {/eq}

{eq}Q= 100 units {/eq}

When the MR function will touch the Quantity axis, MR will be zero

{eq}0= 350 - 7Q. {/eq}

{eq}350 = 7Q. {/eq}

{eq}Q= 50 units {/eq}

This is shown in the graph below

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