Having discussed the different degr

Having discussed the different degrees of price discrimination, bases for segmenting markets, and some practical examples, we can now move on to a more detailed quantitative analysis of the situation.

10.4.4 Analysis
Consider the following situation:

SP10.1 Price discrimination
Valair is an airline flying a particular route that has seasonal demand. The firm’s total demand is given by:
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where Q is the number of passengers per year, in thousands, and P is the fare (in £). In the peak season the demand is given by:
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and in the off-season the demand is given by:
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assume that fixed costs are £6 million per year and that marginal costs are constant at £60 per passenger. Thus the cost function is given by:
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where C is total costs (in £’000).
a. Calculate the profit-maximizing price and output without price discrimination, and the size of the profit.
b. Calculate the profit-maximizing price and output with price discrimination, and the size of the profit.
c. Calculate the demand elasticities of the two segments at their profit-maximizing prices.

Solution
a. Without price discrimination
Reviewing the procedure described in Chapter 8:
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b. With price discrimination
We now examine each segment in turn:
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In order to obtain the size of the profit it is necessary to calculate total revenue and subtract total costs. Note that it is incorrect to compute the profits in each segment separately and then add them together. This would double-count the fixed costs.
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c. The demand elasticities in each segment can also be obtained using
the point elasticity formula:
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At this point a number of general conclusions can be drawn from comparing the situation with price discrimination and the situation without price discrimination:
1 Total output is the same in both situations (note that this is not true if the cost function is non-linear).
2 The prices with discrimination ‘straddle’ the price without discrimination, meaning that one is higher and the other is lower. If there are more than two market segments one or more prices will
always be higher and one or more prices will always be lower.
3 The segment with the higher price will have less elastic demand and vice versa.
4 Profit is always higher under price discrimination. This is because some of the consumer surplus is transferred to producer surplus, as seen earlier.