Question

Price Discrimination - Second-degree price discrimination forces people to reveal their reservation prices. Do you agree? - Derive the condition: P1(1+1/e1) = P2(1+1/ez). How might this expression help a firm that is deciding whether to price discriminate?

Answer 1

- Reservation prices are highest prices that a buyer is willing to pay. It is the first degree price discrimination that forces the consumers to reveal their reservation prices. However, the second degree price discrimination doesn't forces the consumer to reveal their reservation prices. In this competition, firms do not have detailed information about their consumers.

Second Degree price discriminating monopolist derive the reservation prices through law of diminshing marginal utility of consumers/buyers. Monopolist uses this information and charges different prices to the different number of units that a consumer purchases. So, this competition does not forces the consumer to reveal their reservation prices.

- In third degree price discrimination, MR1 = MC in first market and MR2 = MC in second market.

In monoploy, we know that, at equilibrium, MR = MC

TR (total revenue) = P*Q

MR = P + Q(dp/dQ)

MR = P * [1 + (Q/P) * (dP/dQ)]

MR = P * [1 + (1/e)]

So, in first market,

MR1 = P1 * [1 + (1/e1)] -----equation 1

for second market,

MR2 = P2 * [1 + (1/e2)] -----------equation 2

where e = elasticity of demand = p/Q * dQ/dP

at equilibrium, MR1 = MR2 = MC

So, using equatio 1 and equation 2

P1 * [1 + (1/e1)] =   P2 * [1 + (1/e2)] ---Proved

This expression helps the monopolist in terms of charging an optimum price in a market based on its elasticity of demand.

Price will be charged high where the elasticity of demand is high and vice versa.

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