Question 3: (15 marks) A newly established wildlife reserve in Namibia is trying to determine the price it should charge for day visitor tickets. Based on data from their tourism board the management decides to distinguish between foreign and local visitors. The following provides the estimated demand curves for foreign QF and local QL visitors: Q_{F}=750-5P, Q_{L}=150-3 P 3.1 Assume that, for a start, they decide to charge N$30 per ticket. Graphically illustrate the demand curves for both foreign and local visitors. 3.2 Using the price and quantities as calculated in 3.1 above, calculate the price elasticity of demand for each group (use point elasticity). (4) Will the reserve be maximizing its profit at the given price? Explain your answer by using the elasticities you calculated in the previous question. Calculate what price management should be charging foreigners in order to maximize revenue collected from ticket sales? (hint: Use the formula for elasticity and set it equal to -1)

**3.1 Graphical Illustration** The demand curves for foreign and local visitors are: - **Foreign Visitors:** \( Q_{F} = 750 - 5P \) - **Local Visitors:** \( Q_{L} = 150 - 3P \) At \( P = 30 \): - Foreign: \( Q_{F} = 750 - 5(30) = 600 \) - Local: \( Q_{L} = 150 - 3(30) = 60 \) **Graph Details:** - **Foreign Demand Curve:** Starts at \( Q=750 \) when \( P=0 \) and ends at \( Q=0 \) when \( P=150 \). - **Local Demand Curve:** Starts at \( Q=150 \) when \( P=0 \) and ends at \( Q=0 \) when \( P=50 \). At \( P = 30 \): - Foreign: \( Q=600 \) - Local: \( Q=60 \) --- **3.2 Price Elasticity and Revenue Maximization** *Foreign Visitors:* - Elasticity \( E_F = -0.25 \) - Since \( |E_F| < 1 \), increasing the price would increase revenue. *Local Visitors:* - Elasticity \( E_L = -1.5 \) - Since \( |E_L| > 1 \), decreasing the price would increase revenue. **Revenue Maximization for Foreign Visitors:** Set elasticity \( E_F = -1 \): \[ -5 \cdot \frac{P}{750 - 5P} = -1 \] Solving for \( P \): \[ P = 75 \] **Conclusion:** To maximize revenue from foreign visitors, the reserve should charge \( \$75 \) per ticket.