Demand, Supply and Elasticity: Question 10

Worked solution

Part (a): How price elasticity of demand predicts the effect on total revenue

Total revenue is price multiplied by quantity, $TR = P \times Q$. When price rises, quantity demanded falls, so whether total revenue rises or falls depends on which of the two percentage changes is larger:

• If demand is price elastic (the size of PED is greater than 1), the percentage fall in quantity demanded is larger than the percentage rise in price, so the loss of revenue from selling fewer tickets outweighs the gain from the higher price per ticket, and total revenue falls.
• If demand is price inelastic (the size of PED is less than 1), the percentage fall in quantity demanded is smaller than the percentage rise in price, so the gain in revenue from the higher price per ticket outweighs the loss from selling fewer tickets, and total revenue rises.

By estimating the size of PED for its evening tickets, the cinema chain can predict not just that a price rise will change quantity demanded, but the direction in which its total ticket revenue is likely to move. Information it needs before deciding whether to go ahead with the price rise.

Part (b): How complete a guide is price elasticity of demand alone?

Price elasticity of demand is a genuinely useful starting point: as shown in part (a), knowing whether demand is elastic or inelastic tells the chain the direction in which total revenue should move following a price rise, and the size of PED gives a rough sense of how large that change might be. To this extent, PED is a valuable and directly relevant tool for this pricing decision.

However, relying on PED alone has real limitations:

• Reliability of the estimate itself. A PED value is normally estimated from how quantity demanded responded to past price changes, which are often smaller than the price rise now being considered. There is no guarantee that the same responsiveness will apply to a bigger price change, so the predicted effect on revenue could differ from what actually happens.
• Cross elasticity of demand with substitutes. The size of PED depends partly on how many close substitutes are available, and this can change over time. Growth in home streaming services, or a rival cinema chain opening nearby, would make demand for this chain’s tickets more responsive to a price change than an older PED estimate suggests, because a positive cross elasticity between cinema tickets and these substitutes means customers can now switch away more easily. An estimate that ignores this could understate how much revenue actually falls (or how little it rises).
• Income elasticity of demand. If average household income also changes around the same time as the ticket price rise (for example, during an economic downturn) quantity demanded will be affected by both the price change and the income change together. Since PED assumes other things are held equal, it cannot on its own separate out how much of any change in ticket sales is really due to the price rise rather than to changing incomes.

Taken together, price elasticity of demand gives the cinema chain a useful and economically sound starting point for predicting the direction of the revenue effect from a ticket price rise, but it is not a complete or fully reliable guide on its own: the true outcome also depends on how accurately the PED estimate transfers to a larger price change, how cross elasticity of demand with evolving substitutes affects responsiveness, and whether income elasticity effects are operating on quantity demanded at the same time.

Final answers

• (a) If demand is price elastic, a price rise reduces total revenue (the percentage fall in quantity demanded outweighs the percentage price rise); if demand is price inelastic, a price rise increases total revenue (the percentage fall in quantity demanded is smaller than the percentage price rise).
• (b) PED alone is a useful but incomplete guide: it gives the right direction of the revenue effect in principle, but its reliability is limited by uncertainty in the estimate itself, by changing cross elasticity of demand as substitutes such as streaming services evolve, and by the confounding effect of income elasticity of demand if incomes change at the same time.