Question

In: Economics

Example 4: Suppose that the monopolist faces a demand curve for its widgets as q =...

Example 4:

Suppose that the monopolist faces a demand curve for its widgets as q = 9 - 0.2p. The firm’s marginal revenue and cost functions are: MR(q) = 45 – 10q and MC(q) = 15 + 5q. The firm’s total cost function is C(q) = 2.5q2 + 15q + 3.

  1. How many widgets should the firm produce and sell so that the monopolist can maximize its profits?
  2. How much should the firm charge to each of its customers so that the firm can maximize its profits?
  3. How much will the firm earn in total sales (or total revenues)?
  4. How much will the firm earn in total profits?

Solutions

Expert Solution

q = 9 - 0.2p

0.2p = 9 - q

p = 45 - 5q

TR = pq  

TR = (45 - 5q)q

TR = 45q - 5q2  

dTR/dq = 45 - 10q

MR = 45 - 10q

C(q) = 2.5q2 + 15q + 3

MC = 5q + 15  

a)

Profit Maximising condition

MR = MC

45 - 10q = 5q + 15

45 - 15 = 5q + 10q

30 = 15q

q = 2

Therefore the firm should sell 2 widgets to maximise its profit.

b)

p = 45 - 5q

p = 45 - 5(2)

p = 45 - 10

p = 35

So the firm should charge $ 35 to maximise its profit.

c)

TR = pq

TR = 35(2)

TR = 70

The firm will earn $70 in total sale or total revenue.  

d)

Total profit   = TR - C(q)  

= pq -  2.5q2 -  15q -  3

= 35(2) - 2.5(2)2 - 15(2) - 3  

= 70 - 10 - 30 - 3  

= 27

The firm will earn $ 27 in total profits.


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