Question

Suppose, market demand p = 200 - 5q, and SRTC = 20q + 100. Find the equilibrium price (p*) and quantity (q*) in the monopoly. Show your work step by step

Answer 1

Solution: The market demand function of monopoly is given as :

p = 200 - 5q

And total cost function is

TC = 20q +100

Equilibrium condition in case of monopoly is:

P>MC =MR

To determine MC ( marginal cost), differentiate TC with respect to q.

So MC = dTC/dq = 20

To determine MR (marginal revenue), we need to differentiate total revenue (TR) with respect to q. The total revenue equation will be

TR = pq = 200q - 5q²

MR =dTR/dq=200 - 2(5)q

MR = 200- 10Q

Now equate MR and MC to determine equilibrium quantity which is q*.

MR=MC

200-10q = 20

q*= 18

Hence, equilibrium quantity is 18 units.

To determine equilibrium price p* , put the value of q=18 in market demand equation as shown below:

p* = 200 - 5q*

p* = 200- 5(18)

p* = 110

Equilibrium price is $110.