Question

As the manager of a monopoly, you face potential government regulation. Your inverse demand is P = 40 -2Q, and your costs are C(Q) = 8Q

a. Determine the monopoly price and output.

b. Determine the socially efficient price and output.

c. What is the maximum amount your firm should be willing to spend on lobbying efforts to prevent the price from being regulated at the socially optimal level?

Short answer

a.The monopoly price is $24, and the relevant output is 8 units.

b. The socially efficient price is $8and the relevant output is 16 units.

c. The maximum amount of money that can be spent is $128.

Step-by-step solution

Define Monopoly

Monopoly signifies the market where the seller is only one. The monopolist sells unique kind of products which help to earn endless profits.

Explanation

a.

A monopoly firm produces at the point where its marginal revenue equals its marginal costs. With an inverse demand function, marginal income and marginal costs can be calculated.

In this case the marginal revenue curve is twice as steep as the demand curve. To find the marginal revenue, the number that affects the slope of the demand curve should be multiplied by 2, which is the number in front of a variable Q.

$$\begin{gathered} \text{P = 40 - 2Q} \\ \text{MR = 40 - 4Q} \end{gathered}$$

The first derivation of the cost function is used to compute marginal costs:

localid="1657537195664" $$\begin{gathered} C\left(Q\right)=8Q/\frac{\delta C}{\delta Q} \\ MC=8 \end{gathered}$$

So,

localid="1657537200720" $$\begin{gathered} P=MC \\ 40‐4Q=8 \\ 4Q=40-8 \\ 4Q=32 \\ Q=8 \\ P=40-2Q \\ P=40-2\times 8 \\ P=40-16 \\ P=24 \end{gathered}$$

Therefore, localid="1657537206174" $Q=8$and localid="1657537211481" $P=\cancel{S}24$.

Explanation

$\left(a\right)$

When the price of the demand curve equals the company's marginal costs, the socially effective price and output are determined:

localid="1657537220108" $$\begin{gathered} P=MC \\ 40‐2Q^s=8 \\ 2Q^s=40-8 \\ 2Q^s=32 \\ {Q}^s=16 \\ {P}^s=40-2Q \\ {P}^s=40-2\times 16 \\ {P}^s=40-32 \\ {P}^s=8 \end{gathered}$$

Therefore, localid="1657537225254" $Q^s=16$and localid="1657537230469" $P^s=\cancel{S}8$.

Explanation

$\left(b\right)$

The company shall spend the maximum amount of money on lobbying activities equal to their revenue when the price is uncontrolled minus the costs of the goods delivered at the unregulated pricing:

$$\begin{gathered} P_{lobbying}=P^M\times Q^M‐C\left(Q^M\right) \\ =8\times 24‐8\times 8 \\ =192‐64 \\ =128 \end{gathered}$$

The maximum amount of money that the company should spend on lobbying is $\cancel{S}128$.