You are the manager of a company that produces a product according to the cost f

Question

You are the manager of a company that produces a product according to the cost function C(qi) = 160 + 58qi – 6qi2 + qi3.

a. You operate a perfectly competitive business. Which choice below represents the short-run supply function? Be sure to explain the calculation or reasoning (as applicable) behind your choice.
P = 35 - 15q + 3q2 if P is greater than or equal to $52; otherwise the firm produces zero units

P = 40 - 8q + 2q2 if P is greater than or equal to $55; otherwise the firm produces zero units

There is no supply curve in this case

P = 58 - 12q + 3q2 if P is greater than or equal to $49; otherwise the firm produces zero units

b. You operate a monopoly. Which choice below represents the short-run supply function? Be sure to explain the calculation or reasoning (as applicable) behind your choice.

P = 40 - 8q + 2q2if P is greater than or equal to $55; otherwise, the firm produces zero units.

P = 35 - 15q + 3q2 if P is greater than or equal to $52; otherwise it produces zero units.

P = 58 - 12q + 3q2 if P is greater than or equal to $49; otherwise, the firm produces zero units

There is no supply curve in this case

c. You operate a monopolistically competitive business. Which choice below represents the short-run supply function? Be sure to explain the calculation or reasoning (as applicable) behind your choice.

There is no supply curve in this case

P = 35 - 15q + 3q2 if P is greater than or equal to $52; otherwise, the firm produces zero units

P = 40 - 8q + 2q2 if P is greater than or equal to $55; otherwise, the firm produces zero units

P = 58 - 12q + 3q2 if P is greater than or equal to $49; otherwise, the firm produces zero units

Explanation / Answer

(a) Ans: There is no supply curve in this case

Explanation:

A perfectly competitive firm’s supply curve is the marginal cost curve above the minimum of its AVC curve.

Here, MCi = 58 - 12qi +3qi2

         AVCi = 58qi – 6qi2 + qi3 / qi = 58 - 6qi + qi2

Since MC and AVC are equal at the minimum point of AVC, set MCi = AVCi

58 - 12qi +3qi2 = 58 - 6qi + qi2

=> 58 - 12qi +3qi2 - 58 + 6qi - qi2 = 0

=> 2qi2 - 6qi = 0

=> 2qi(qi - 3) = 0

=> 2qi = 0

=> qi = 0

OR

qi - 3 = 0

=> qi = 3

Thus, AVC is minimized at an output of 3 units, and the corresponding AVC is:

   AVCi = 58 - 6(3) + (3)2 = 31

Thus the firm’s supply curve is described by the equation MCi = 58 - 12qi +3qi2 if P is greater than or equal to $31, otherwise, the firm produceszero units.

(b) Ans: There is no supply curve in this case

Explanation:

A monopolist produces where MR = MC and thus does not have a supply curve.

(c) Ans: There is no supply curve in this case

Explanation:

A monopolistically competitive firm produces where MR = MC and thus does not have a supply curve.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.