Question

You are the manager of a monopoly that faces a demand curve described by P = 85 − 5Q. Your costs are C = 20 + 5Q. The profit-maximizing output for your firm is:

Answer 1

Given:

Price function : P = 85 − 5Q.

Cost function : C = 20 + 5Q.

To find:

The profit-maximizing output for your firm.

Explanation:

Total revenue = Price × Quantity

$TR=P\times Q$

$TR=(85-5Q)\times Q$

$TR=85Q-5Q^2$

Differentiate with respect to quantity.

$\dfrac{d(TR)}{dQ}=85(1)-5(2Q)$

$MR=85-10Q$

Cost function is

$C=20+5Q$

Differentiate with respect to quantity.

$\dfrac{dC}{dQ}=(0)+5(1)$

$MC=5$

The profit is maximum if $MR=MC$.

$85-10Q=5$

$85-5=10Q$

$80=10Q$

Divide both sides by 10.

$\dfrac{80}{10}=Q$

$Q=8$

Therefore, the profit-maximizing output for the firm is 8 units.

Answer 2

The demand curve is the curve that shows the relationship of demand with its various aspects. The demand curve is the graphical presentation of the shifts that are caused by the aspects of the demand.

The given information are:

Price function : P = 85 − 5Q.

Cost function : C = 20 + 5Q.

Total revenue = Price × Quantity

$TR=P\times Q$

$TR=(85-5Q)\times Q$

$TR= 85Q-5Q^{2}$

Differentiate with respect to quantity.

$\frac{d(TR)}{dQ} =85(1)-5(2Q)\\MR=85-10Q$

Cost function is=$C=20+5Q$

Differentiate with respect to quantity.

$\frac{dC}{dQ}=(0)+5(1)\\MC=5$

The profit is maximum in the firm if:  $MR=MC$

$85-10Q-5\\85-5=10Q\\80=10Q$

Divide both sides by 10.

$\frac{80}{10}=Q\\Q=8$

Therefore, the profit-maximizing output for the firm is 8 units.

To know more about the calculation of the profit maximization, refer to the link below:

https://brainly.com/question/7145210