**Suppose you are a 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’ve determined that reducing the price of an average meal to $18 would increase the quantity demanded to 450 per day. Would you expect total revenue to rise or fall as a result of this second price reduction? Explain. Compute total revenue at the three meal prices. Do these totals confirm your expectations?**

The question you are asking is an example of price elasticity of demand: how the quantity demanded of a product or service rises or falls in response to a change in the price of that product or service, all else being equal.

The restaurant in question serves an average of 400 meals per day at an average price of $20 per meal. That equates to $8,000 of revenue per day on average (400 meals x $20 average price per meal = $8,000).

However, the survey of the customer base indicates that by reducing the price of an average meal to $18, the quantity demanded would rise to 450 per day from 400 before. In this case, the average revenue per day rises to $8,100, despite the reduction in price per meal. There are now 450 meals being sold at the $18 price or (450 x $18 average price per meal = $8,100).

Thus, total revenues rise even though the manager has reduced the price. Think of it this way: the price decline of 10% was more than offset by a 12.5% increase in the unit volume or quantity of meals being served.

Your question mentions only two prices—the original $20 per meal and then the reduced $18 per meal—so it is somewhat difficult to answer the second part of the question. However, it is fairly easy to plug numbers in to see the outcome.

At a certain point, there will likely be diminishing returns on price reductions. In other words, the manager cannot stimulate enough increased demand to fully offset the price decline indefinitely. For instance, if we use the numbers $16 and 480 for the price of the meal and units sold, respectively, we see that a 20% drop in the price from the original $20 does not fully offset a 20% volume drop from the original 400 units. In this case, the total revenue is only $7,680, a 4% decline from the initial $8,000.

**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.**

Price elasticity of demand is used as

an economic measure of the change in the quantity demanded or purchased of a product in relation to its price change (Investopedia).

Some goods are very elastic, meaning that changes in price drastically affect how much of them people want to buy; some goods are not elastic, meaning people will buy the same amount of them no matter how much they cost. For example, whether gas is $1.97/gal or $3.05/gal, most people will still be buying the same amount of gas for their commute to work; price will not affect demand. However, way more people will want to buy a PlayStation 5 if they can get it brand-new for $50.

Price elasticity of demand is calculated as:

% Change in Quantity Demanded / % Change in Price.

And % Change is calculated as:

(# of Increase/Decrease / Original Number) * 100.

Our Original Qty, or Qty0, is 400, and Original Price, or Price0, is $20.

Our new quantity, or Qty1, is 450. Our new price, or Price1, is $18.

The prompt asks us to compute the price elasticity of demand between these two points. So we need to determine the percent change for quantity and price, divide % change in quantity by % change in price, and compare the two options.

Let's start with Qty1/Price1.

- The change from Qty0 to Qty1 is 50. The percent change is calculated as
50/400=0.125, and then 0.125*100=
**12.5%**. - The change from Price0 to Price1 is $2. The percent change is calculated as
2/20=0.1, and then 0.1*100=
**10%**. - Following the price elasticity of demand formula, divide percent change in
quantity by % change in price. The price elasticity of demand is calculated as
12.5%/10%=
**1.25**.

The price elasticity of demand is 1.25. This means that the more you lower the price, the more people will want to buy it, by a factor of 1.25.

Based on our answer for the first question you asked, we are asked to find whether total revenues would rise or fall if we lowered the average price of a meal.

Originally, 400 people were ordering a meal every day. At an average price
of $20, that means the daily revenue was roughly **$8000/day**
(400*20=8000).

If prices are lowered to an average of $18, 450 people are now ordering
every day. 450*18=**$8100/day**.

If prices are lowered, revenue will increase because 8100 is greater than 8000.

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