Question

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 (b) and (d) above?

Answer 1

Price elasticity of demand= (Change in Q/Change in P) x initial P/initial Q

The relationship between price and elasticity of demand(Ed):

• If Ed>1, then price and total revenue move in opposite direction.
• If Ed<1, then price and total revenue move in same direction.
• If Ed=1, then there will be no change in total revenue due to a change in price.

Initial price= 20

Initial quantity= 400

New price= 18

New quantity= 450

Change in price= -2

Change in Q= 50

Ed= (50/-2) x 20/400= -25/20= (-)1.25

Here in absolute term Ed>1, so as price decreases there will be a increase in total revenue.

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Initial price= 18

Initial quantity= 450

New price= 16

New quantity= 500

Change in price= -2

Change in Q= 50

Ed= (50/-2) x 18/450= (-)1

Here in absolute term Ed=1, so as price decreases there will be a no change in total revenue.

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When P= 20, Q= 400:

Total revenue= 20 x 400= 8000

When P= 18, Q= 450:

Total revenue= 18 x 450= 8100 (total revenue increases)

When P= 16, Q= 500:

Total revenue= 16 x 500= 8000 (total revenue remain same from initial point)

Yes, conclusion about total revenue was correct.