Q5. A government is planning to organise public fireworks. Their analysists split the population of the country into 2 groups based on income. They estimated the willingnessto-pay curves for both groups: 1 = 5 0.51 ,2 = 1 0.252 , where Q is the length of the show. The marginal costs of organising a fireworks show of length are = 9 16 2 , and there is also a fixed cost of 4 9 associated with the event.

a) Derive the total willingness-to-pay curve. Plot it on a graph together with the groupspecific willingness-to-pay curves. [4 marks]

b) Find the optimal length of the fireworks show [3 marks]

c) What happens to the optimal length of a fireworks show as the population changes? What about as average income levels change? What happens to the optimal length as the fixed or marginal costs change? [3 marks]