## Tuesday, 24 May 2016

### Why block pricing doesn't work for heterogeneous demand

On Sunday I covered two-part pricing. Today it's the turn of block pricing. A firm uses block pricing when it charges a relatively high price until the consumer reaches some threshold, then a lower price for units after the threshold. In reality, there could be multiple thresholds. Buy-one-get-one-half-price is an example of block pricing. As with two-part pricing, we can think about block pricing first by contrasting it with a monopoly firm pricing at a single price-per-unit, as in the diagram below (for simplicity, I'll again use a constant-cost firm).

The monopoly firm using a single price-per-unit selects the price that maximises profits. This occurs where marginal revenue is equal to marginal cost, i.e. at the quantity Q1 with price P1. The producer surplus (profit) the firm earns is the rectangular area CBDF.

However, if the firm switches to block pricing, then the firm can choose an initially higher price (P0), at which point the consumers purchase Q0 of the good. If the firm lowers the price to P1 for every unit the consumer buys after Q0, then the consumer will buy Q1 of the good (and pay P0 for the first Q0 units, then P1 for the rest). The firm's profits would increase by the area HGJC.

The firm could block again, offering a lower price than P1 for units purchased beyond Q1, and capture more profits (I haven't shown this on the diagram though). Again, this demonstrates that firm profitability is all about creating and capturing value.

We can also show the effect of block pricing using the consumer choice model. This is illustrated in the diagram below. The black budget constraint represents the most the consumer can afford to buy with their income, when there is a single price-per-unit for Good X (with 'All Other Goods' [AOG] on the y-axis). The consumer purchases the bundle of goods E, which includes X0 of Good X, and A0 of All Other Goods.

With block pricing, the firm charges the standard price Px up to the quantity X0, then pays a lower price beyond that quantity. This causes the budget constraint to pivot outwards (and become flatter) from the point E. So this consumer can now reach a higher indifference curve, by buying the bundle of goods D (their new best affordable choice). This bundle includes more of Good X (X1), and less of All Other Goods (A1). Because they are buying less of All Other Goods, they must be spending more on Good X.

As with two-part pricing, block pricing also works well when the firm faces homogeneous demand for its product (i.e. when all consumers have similar demand for the product). We can also use the consumer choice model to demonstrate why block pricing doesn't work so well when there is heterogeneous demand.

Consider two consumers - one with low demand (shown on the diagram below with the blue indifference curve), and one with high demand (red indifference curves). With a single price-per-unit, the low demand consumer buys Bundle G, which includes X1 of Good X, and A1 of All Other Goods, and the high demand consumer buys Bundle J, which includes X3 of Good X, and A3 of All Other Goods.

When the firm moves to block pricing instead, the low demand consumer is not affected. The highest indifference curve they can get to is still I0, so they continue to buy Bundle G.

The high demand consumer would be better off moving to buying Bundle K, which is on the highest indifference curve they can now reach. Bundle K contains more of Good X (X4), so block pricing does induce these consumer to buy more. However, Bundle K includes more of Good A (A4), which means that even though these high demand consumers are buying more of Good X with block pricing, they are actually spending less on Good X.

So, block pricing doesn't work so well for heterogeneous demand, because the lowest demand consumers will not be affected, while the highest demand consumers will buy more of the good, but spend less on it. The combination of these two effects is likely to reduce the firm's profit, but notice that it isn't as bad as for two-part pricing that I described on Sunday.

Again, this is why you don't often see block pricing (or two-part pricing) alone 'in the wild'. Firms must first ensure they have relatively homogeneous demand, and they achieve this through price discrimination (e.g. through menu pricing - offering different options to different consumers, knowing that each option will appeal to a different 'type' of consumer). Then within each homogeneous group they can use block pricing or two-part pricing.

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