Question

This question is very important and I need solution for this issue with all the details a.b.c , and help me with all the details? BR/Ha

a) Find the profit maximizing total output and how much of it that is sold on market A and market B respectively if the monopoly uses third degree price discrimination. What prices will our monopolist charge in the two separate markets?A monopolist faces two totally separated markets with inverse demand p=100 – qA and p=160−2qB respectively. The monopolist has no fixed costs and a marginal cost given by mc= 2/3 q .

b) Calculate the price elasticity of demand in each market and explain the intuition behind the relationship between the prices and elasticities in these two separate markets.

c)Use the definition of marginal revenue and the definition of the price elasticity of demand to derive an expression for the markup for a monopolist. Use this expression to calculate the markup for the two separate markets in question 4a).

Answer 1

a). In case of third degree price discrimination, the monopolist separates the markets on the basis of elasticity of demand and accordingly sets different prices in different markets.

In the above question, there are two markets - market A and market B. The inverse demand functions are as follows:

p=100-qA and p=160-2qB (where qA and qB are the quantity of A and B respectively)

Also, MC = 2/3q

We need to find the optimum level of output. This can be calculated by using the below condition:

Marginal revenue (MR) = Marginal Cost (MC)

TR_A = Price of A * Quantity of A

= (100-qA)*qA = 100qA-qA²

MR_A= TR_A/qA = 100-2qA

Similarly,

TR_B= Price of B * Quantity of B

= (160-2qB)*qB = 160qB-2qB²

MRB = TRB/qB = 160-4qB

Condition for maximization = MR_A = MR_B = MC

When MR_A = MC

100-2qA = 2/3 (qA+qB)

= 300 -6qA = 2qA + 2qB

= 8qA + 2qB = 300 => 4qA + qB = 150 .....(i)

When MR_B = MC

160-4qB = 2/3(qA+qB)

= 240-6qB = qA + qB => qA + 7qB =240 .....(ii)

Solving (i) and (ii), we get,

qA = 30 units and qB = 30 units

Explanation:

Total output produced = qA +qB = 30+30 = 60 Units

Price charged by the monopolist in market A :

p=100-qA = 100-30 = 70

Price charged by the monopolist in market B :

p=160-2qB = 160-2(30/) =160-60 = 100

b). Elasticity in market A given price = 70 and quantity = 30

p = 100 - qA (given)

qA = 100 - p

qA/P = -1

We know elasticity (eA) = (qA/p) * (p/qA)

eA = -1 * 70/30 = -2.33

Similarly,elasticity in market B given price = 100 and quantity = 30

p = 160 -2 qB (given)

qB = (160-p)/2

qB/P = -1/2

We know elasticity (eB) = (qB/p) * (p/qB)

eB = -1/2 * 100/30 = -1.66

It can clearly be seen that the elasticity in market A is more than elasticity in market B. And in order to be profitable, a monopolist will always charge a less price in the market with high elasticity which is evident from the price in market A, that is $70 which is less than $100 charged in market B. This is because, the elasticity in market A being more, fall in demand will be more in market A if price increases as compared to market B. Also, market B being less elastic, the change in demand will not be more even if higher price is charged.

Therefore, the monopolist charges prices in separate markets depending upon the elasticity - higher price in less elastic market and lower in more elastic market.

c). We know the mark up of a monopolist is given by (P-MC)/P

Where, P is the price and MC is the marginal cost. This can be derived as follows:

Now we can calculate markup in two markets: (using values of eA and eB from b).)

Market A = -1/eA = -1/(-2.33) = 0.429 or 42.9%

Market B = -1/eB = -1/(-1.66) =0.6024 or 60.24%