The price elasticity of demand

 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?

To compute the price elasticity of demand between two points, you can use the following formula:

PED = (% Change in Quantity Demanded) / (% Change in Price)

In this case, the initial quantity demanded (Q1) is 400 meals per day, the initial price (P1) is $20, the new quantity demanded (Q2) is 450 meals per day, and the new price (P2) is $18.

First, calculate the percentage changes:
% Change in Quantity Demanded = ((Q2 - Q1) / Q1) * 100

% Change in Price = ((P2 - P1) / P1) * 100
% Change in Quantity Demanded = ((450 - 400) / 400) * 100 = 12.5%

% Change in Price = (($18 - $20) / $20) * 100 = -10%

Now, use these values to calculate the price elasticity of demand:
PED = (12.5% / -10%) = -1.25
The price elasticity of demand between these two points is -1.25.

With a price elasticity of demand of -1.25, this means that demand is relatively elastic (elasticity greater than 1). When you reduce the price, the percentage increase in quantity demanded is greater than the percentage decrease in price. Therefore, you would expect total revenues to rise because the increase in the number of meals sold will more than offset the decrease in price.

To compute the price elasticity of demand between the new points, where the price is $16 and the quantity demanded is 500 meals per day, you can use the same formula as in question 1:
PED = (% Change in Quantity Demanded) / (% Change in Price)
Q1 = 450 meals per day, P1 = $18

Q2 = 500 meals per day, P2 = $16
Calculate the percentage changes:
% Change in Quantity Demanded = ((500 - 450) / 450) * 100 = 11.11%

% Change in Price = (($16 - $18) / $18) * 100 = -11.11%

Now, calculate the price elasticity of demand:
PED = (11.11% / -11.11%) = -1
The price elasticity of demand between these two points is -1.

With a price elasticity of demand of -1, demand is unitary elastic (elasticity equals -1). A unitary elastic demand means that the percentage change in quantity demanded is exactly equal to the percentage change in price. Therefore, a further reduction in price from $18 to $16 would result in no change in total revenue because the increase in quantity demanded would offset the decrease in price.

To compute total revenue at the three meal prices, you can use the following formula:
Total Revenue = Quantity Demanded × Price

At $20 per meal and 400 meals per day:

Total Revenue = 400 meals/day × $20/meal = $8,000/day

At $18 per meal and 450 meals per day:

Total Revenue = 450 meals/day × $18/meal = $8,100/day

At $16 per meal and 500 meals per day:

Total Revenue = 500 meals/day × $16/meal = $8,000/day

These totals confirm the answers in (b) and (d) above:

When the price decreased from $20 to $18, total revenue increased.

When the price decreased from $18 to $16, total revenue remained the same.