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WA2. Elasticity of Demand

Statement

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.

Question 1

Compute the price elasticity of demand between these two points.

The price elasticity of demand is given by the formula (Rittenberg & Tregarthen, 2009).

\[ \text{Price Elasticity of Demand} = \frac{\frac{∆Q}{\bar{Q}}}{\frac{∆P}{\bar{P}}} \]

Where:

  • Q is the quantity demanded, and ∆Q is the change in quantity demanded. \(\bar{Q}\) is the average quantity demanded.
  • P is the price, and ∆P is the change in price. \(\bar{P}\) is the average price.

Given that the quantity demanded increases from 400 to 450, and the price decreases from $20 to $18, we can calculate the price elasticity of demand as follows:

\[ ∆Q = 450 - 400 = 50 \\ \bar{Q} = \frac{450 + 400}{2} = 425 \\ ∆P = 18 - 20 = -2 \\ \bar{P} = \frac{18 + 20}{2} = 19 \\ eD = \frac{\frac{50}{425}}{\frac{-2}{19}} = \frac{0.1176}{-0.1053} = -1.1176 \]

Therefore, the price elasticity of demand between these two points is eD =-1.1176.

Question 2

Would you expect total revenues to rise or fall? Explain.

The absolute value of the price elasticity of demand is 1.1176 > 1, which means that the demand is elastic.This means that demand changes by a larger percentage than the price change (aka, demands changes a lot with price), and the total revenue will change in the demand’s direction and opposite to the price direction (Rittenberg & Tregarthen, 2009).

We noticed that the demand has increased, therefore, total revenue will rise.

Question 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.

Given that the quantity demanded increases from 450 to 500, and the price decreases from $18 to $16, we can calculate the price elasticity of demand similarly to the previous question:

\[ ∆Q = 500 - 450 = 50 \\ \bar{Q} = \frac{500 + 450}{2} = 475 \\ ∆P = 16 - 18 = -2 \\ \bar{P} = \frac{16 + 18}{2} = 17 \\ eD = \frac{\frac{50}{475}}{\frac{-2}{17}} = \frac{0.1053}{-0.1176} = -0.8947 \]

Question 4

Would you expect total revenue to rise or fall as a result of this second price reduction? Explain.

The absolute value of the price elasticity of demand is 0.8947 < 1, which means that the demand is inelastic. This means that demand changes by a smaller percentage than the price change (aka, demands changes a little with price), and the total revenue will change in the price’s direction and opposite to the demand’s direction (Rittenberg & Tregarthen, 2009).

We noticed that the price has decreased, therefore, total revenue will fall.

Question 5

Compute total revenue at the three meal prices. Do these totals confirm your answers in (b) and (d) above?

Total revenue is calculated as the product of the price and quantity demanded. We can calculate the total revenue at the three meal prices as follows:

TR(A) at point A (P = $20, Q = 400), TR(B) at point B (P = $18, Q = 450), and TR(C) at point C (P = $16, Q = 500).

\[ TR(A) = 20 * 400 = 8000 \\ TR(B) = 18 * 450 = 8100 \\ TR(C) = 16 * 500 = 8000 \]
  • Between points A and B: Total revenue increased from $8000 to $8100, confirming the answer in (b) above.
  • Between points B and C: Total revenue decreased from $8100 to $8000, confirming the answer in (d) above.
  • Between points A and C: Total revenue remained constant at $8000.

References

  • Rittenberg, L. & Tregarthen, T. (2009). Principles of Economics. Flat World Knowledge.Chapter 5: Elasticity: A Measure of Response. <https://my.uopeople.edu/pluginfile.php/1894532/mod_book/chapter/527770/Principles%20Of%20Economics%20Chapter%2005.pdf>