# Consider a monopolist who is faced with the market demand curve P = 10 - Q. Its total cost is...

## Question:

Consider a monopolist who is faced with the market demand curve P = 10 - Q. Its total cost is given by 2Q.

(a) If the monopolist has to use one price, what would be profit maximizing price?

(b) If the monopolist can use two part tariff, what would be the entrance (to the market) fee and the price for each unit of the good?

(c) What is the difference between (a) and (b) from the perspectives of consumers, monopolists, and the society as a whole?

## Two-Part Tariff

Two-part tariff in monopoly competition is a price discrimination strategy. Monopoly firm in two-part tariff prices their commodities equal to marginal cost and put entry fee for consumer, which equals to their consumer surplus.

Given:

Market demand curve P = 10 - Q

Firm Total cost C = 2Q

Total Revenue (TR) equals to demand multiply by quantity:

{eq}\begin{align*} TR &= P \times Q\\ &= \left( {10 - Q} \right) \times Q\\ &= 10Q - {Q^2} \end{align*} {/eq}

So, the marginal revenue (MR) is:

{eq}\begin{align*} MR &= \dfrac{{d\left( {TR} \right)}}{{d\left( Q \right)}}\\ &= 10 - 2Q \end{align*} {/eq}

Marginal cost (MC) equals to:

{eq}\begin{align*} MC &= \dfrac{{d\left( C \right)}}{{d\left( Q \right)}}\\ &= 2 \end{align*} {/eq}

So, for profit-maximization, MC should be equal to MR. So, at the profit-maximizing condition:

{eq}\begin{align*} MC &= MR\\ 2 &= 10 - 2Q\\ Q &= 4 \end{align*} {/eq}

Putting quantity equals to four at the demand equation:

{eq}\begin{align*} P &= 10 - Q\\ P &= 10 - 4\\ P &= 6 \end{align*} {/eq}

So, price is equal to 6 at the profit-maximizing condition.

b.

If a monopolist use two-part tariff, then it produces where price equals marginal cost so price will be 2 per unit. So, a monopoly will produce: {eq}\begin{align*} P &= MC\\ 10 - Q &= 2\\ Q &= 8 \end{align*} {/eq} So, the producer now produces eight quantities. Producer set the total entry fee equals to consumer surplus (CS). {eq}\begin{align*} CS &= \dfrac{1}{2} \times \left( {10 - 2} \right) \times 8\\ &= 32 \end{align*} {/eq} So, the producer will cost a total32 as an entry fees and \$2 as price per unit quantity.

c.

At B, the consumer surplus reduces to zero because they have to pay their entire consumer surplus as the entry fee. The producer gets better off because they now earn consumer surplus too. And social loss or deadweight loss decrease to zero in two tariff condition because monopoly produces, where price of commodity is equal to marginal cost.