A dealer in deep freezers increased the price of his product from $450 to $500 and sales dropped from 800 units to 600 units a week. Use the information abo...

(a)(i) Price elasticity of demand (PED) measures how responsive quantity demanded is to a change in price. Using the initial values as the base:

\[ PED = \frac{\% \Delta Q}{\% \Delta P} = \frac{\Delta Q / Q_1}{\Delta P / P_1} \]

Here \( \Delta Q = 600 - 800 = -200 \), \( Q_1 = 800 \), \( \Delta P = 500 - 450 = 50 \), \( P_1 = 450 \).

\[ PED = \frac{-200/800}{50/450} = \frac{-0.25}{0.1111} = -2.25 \]

The value is 2.25 (ignoring the negative sign, which merely shows the inverse relationship between price and quantity).

(a)(ii) Type of elasticity. Because \( |PED| = 2.25 > 1 \), demand is elastic: the percentage fall in quantity demanded (25%) is greater than the percentage rise in price (about 11%), so buyers are very responsive to the price change.

(b)(i) Total revenue. \( TR = P \times Q \).

• Before: \( 450 \times 800 = \$360{,}000 \).
• After: \( 500 \times 600 = \$300{,}000 \).

(b)(ii) Change in total revenue. \( 300{,}000 - 360{,}000 = -\$60{,}000 \), a fall of \$60,000.

(c) Effect on total revenue. The price increase caused total revenue to fall by \$60,000. This is exactly what theory predicts: when demand is elastic, a rise in price reduces total revenue because the proportionate loss of sales outweighs the higher price per unit.

(d) Two factors influencing PED: availability of close substitutes (more substitutes make demand more elastic), and the proportion of income spent on the good (goods taking a large share of income tend to have more elastic demand). Other acceptable factors: whether the good is a necessity or a luxury, and the time period allowed for adjustment.