91Ó°ÊÓ

The total revenue is given by multiplying price with quantity. The price of the product is given as $9. Thus, you have:

$$\begin{gathered} TR=p×q \\ =9q \\ MR=\frac{d\left(TR\right)}{dq} \\ =\frac{d\left(9q\right)}{dq} \\ =9 \end{gathered}$$

The optimal level of output is calculated by equating marginal revenue (MR) with marginal cost (MC).

3+2q=9

2q=9-3

2q=6

q=3

The optimal output is 3 units.

A firm’s producer surplus (PS) is the sum of the differences between the price and marginal cost of each unit produced.The marginal cost of each output produced is calculated below:

MC₁($) = 3 + (2 x 1) = 5

MC₂($) = 3 + (2 x 2) = 7

MC₃($) = 3 + (2 x 3) = 9

The producer surplus is calculated below:

PS($) = (p - MC₁) + (p - MC₂) + (p - MC₃)

= (5 - 5) + (7 - 5) + (9 - 5)

=0 + 2 + 4

=6

The producer surplus of the firm is $6.

The average variable cost (AVC) = (3 +q). Putting the value of output (q =3), the value of AVC is $6.

TVC($) = q x AVC

=3 x 6 = 18

TC($) = TVC + FC

= 18 + 3 = 21

TR($) = p x q

= 9 x 3 = 27

Profit($) = TR - TC

= 27 - 21 = 6

The difference between TR and TC is greater than zero. Hence, the firm is earning a positive in the short run. The profit is $6.