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Homework answers / question archive / Suppose you are the manager of a restaurant that serves an average of 400 meals per day at an average price per meal of $20
Suppose you are the manager of a restaurant that serves an average of 400 meals per day at an average price per meal of $20. On the basis of a survey, you have determined that reducing the price of an average meal to $18 would increase the quantity demanded to 450 per day.
1) Compute the price elasticity of demand between these two points.
2) Would you expect total revenues to rise or fall? Explain.
3) Suppose you have reduced the average price of a meal to $18 and are considering a further reduction to $16. Another survey shows that the quantity demanded of meals will increase from 450 to 500 per day. Compute the price elasticity of demand between these two points.
4) Would you expect total revenue to rise or fall as a result of this second price reduction? Explain.
5) Compute total revenue at the three meal prices. Do these totals confirm your answers in (2) and (4) above?
4) As an approximation, with a price elasticity of 1, total revenue would be expected to remain unchanged. This is because the percentage change in quantity demanded is equal in absolute magnitude to the percentage change in price and would offset its negative effect on total revenue.
5) Total Revenue when P is $20 = $20 x 400 = $8,000
Total Revenue when P is $18 = $18 x 450 = $8,100
Total Revenue when P is $16 = $16 x 500 = $8,000
The effect on revenue of the first price fall does confirm the prediction in (2).
The effect of the second price fall does not, however, confirm the prediction in (4) since total revenue decreases even though the price elasticity is 1. It is not uncommon for there to be relatively small discrepancies like this for price changes at or near the unit price elasticity point on the demand curve. The reason for this is simply arithmetical. Consider the following simple example where a price and a quantity are multiplied together to give total revenue: TR = P x Q = 4 x 4 = 16. Now suppose P falls by 25% and Q rises by 25%, then TR = P x Q = 3 x 5 = 15. So, even though price elasticity is 1, TR falls slightly. The arithmetically correct value that Q would have to reach to offset the price fall is 4 / 0.75. = 5.333. This quantity, when multiplied by the new price of 3 would leave TR unchanged at 16.
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