Question

Suppose that a competitive firm’s marginal cost of producing outputqis given by MC(q) = 3 + 2q. Assume that the market price of the firm’s product is \(9.

a. What level of output will the firm produce?

b. What is the firm’s producer surplus?

c. Suppose that the average variable cost of the firm is given by AVC(q) = 3 + q. Suppose that the firm’s fixed costs are known to be \)3. Will the firm be earning a positive, negative, or zero profit in the short run?

Short answer

1. The firm will produce 3 units of output.

2. The firm’s producer surplus is $6.

3. The firm is earning positive profit in the short run.

Step-by-step solution

Calculation of optimal level of output that the firm will produce

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

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

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.

Calculating the firm’s producer surplus

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.

Determining whether the firm is earning positive, negative, or zero profit

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.