No stolen/copied answers please. Suppose a monopoly sells to two identifiably di

Question

No stolen/copied answers please.

Suppose a monopoly sells to two identifiably different types of customers, A and B, who are unable to practice arbitrage. The inverse demand curve for group A is PA = 19 - QA, and the inverse demand curve for group B is PB = 11 - 2QB. The monopolist is able to produce the good for either type of customer at a constant marginal cost of 1, and the monopolist has no fixed costs. If the monopolist is able to practice group price discrimination, what would be the values of the price elasticities of the two groups at the profit maximizing prices?

Explanation / Answer

PA = 19- QA

And MC= 1

Now, for monopoly profit maximisation , condition is MR=MC ,

So, firstly calculate total revenue = PA(QA)

[19 - QA] (QA) = 19 QA - QA2

Marginal revenue = 19 - 2QA

Put MR= MC , we get 19-2QA = 1

QA = 9

Now, put QA =9 in PA then, we get

PA = 19- 9 = 10

To calculate price elasticity at these profit maximsing price and quantity , we need to find the derivative of demand function:

Reform the invesrse demand function, then QA = 19- PA

Change in Q with respect to change in P = -1.

Elasticity =( Change in QA/Change in PA ) (PA/QA)

= (-1) (10/9)

= -10/9

= -1.11 {Value of price elasticity for group A }

Now, for group B

PB = 11- 2QB

MC= 1

Profit maximisation condition is where MR= MC

Total revenue = PBQB

= (11- 2QB)(QB)

= 11 QB - 2QB2

Marginal revenue , MR= 11 - 4QB

MR = MC

11 - 4QB = 1

QB = 2.5

Now put the vale of QB in PB, we get

PB = 11- 2(2.5)

= 11-5 = 6

To calculate the price elasticity of demand at profit maximising price and output firstly calculate the dervivate of demand function :

Reform the inverse demand function : QB = (11 - PB) /2

Now, change in QB/ change in PB = -1/2   

  Elasticity =( Change in QB/Change in PB ) (PB/QB)

= (-1/2) ( 6 / 2.5)

= - 6/5

= -1.2 { Value of price elasticity for group B}

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