1. **State the problem:** We are given the price elasticity of demand (PED) for record players as $-0.4$, the initial price $P_1=150$, the new price $P_2=180$, sales last year $Q_1=600$, fixed costs £15,000, and variable cost per unit £60. We need to analyze the effect of the price increase on quantity demanded, revenue, and profit. 2. **Calculate the percentage change in price:** $$\%\Delta P = \frac{P_2 - P_1}{P_1} = \frac{180 - 150}{150} = \frac{30}{150} = 0.2 = 20\%$$ 3. **Use PED to find the percentage change in quantity demanded:** $$\%\Delta Q = PED \times \%\Delta P = -0.4 \times 0.2 = -0.08 = -8\%$$ 4. **Calculate the new quantity demanded $Q_2$:** $$Q_2 = Q_1 \times (1 + \%\Delta Q) = 600 \times (1 - 0.08) = 600 \times 0.92 = 552$$ 5. **Calculate total revenue before and after the price change:** - Initial revenue: $$TR_1 = P_1 \times Q_1 = 150 \times 600 = 90000$$ - New revenue: $$TR_2 = P_2 \times Q_2 = 180 \times 552 = 99360$$ 6. **Calculate total costs before and after the price change:** - Total variable cost before: $$VC_1 = 60 \times 600 = 36000$$ - Total cost before: $$TC_1 = Fixed + VC_1 = 15000 + 36000 = 51000$$ - Total variable cost after: $$VC_2 = 60 \times 552 = 33120$$ - Total cost after: $$TC_2 = 15000 + 33120 = 48120$$ 7. **Calculate profit before and after the price change:** - Profit before: $$\pi_1 = TR_1 - TC_1 = 90000 - 51000 = 39000$$ - Profit after: $$\pi_2 = TR_2 - TC_2 = 99360 - 48120 = 51240$$ 8. **Interpretation:** - The price increase led to an 8% decrease in quantity demanded. - Total revenue increased from 90000 to 99360. - Profit increased from 39000 to 51240. **Final answer:** The price increase raises profit by £12240 despite a drop in sales volume.