Walley is the sole distributor of fine trumpets in the area. The cost of producing and importing one trumpet is $1,000. Last year, a total of 3,200 trumpets were sold, at a price of $3,000 per unit. This year, they hired a consulting firm which estimated that elasticity of demand for trumpets equals -3, and that thedemand for trumpets is linear.

Construct the demand function. That is, given the information on prices, quantities and price elasticity, give an expression for the demand function.

Hint:Recall that to get a demand curve with this information, use the definition ofa linear demand curve combined with the definition of the priceelasticity of demand.

Using this information, can you help Walley choose the optimal price? How many trumpets would it sell this year?

Before Walley had a chance to rewrite the prices and place the order of trumpets, the same consulting company did a survey and concluded thathalfof customers who buy trumpets from us would use Walley for trumpet cleaning services (andthe other halfwould not). The cleaning service has a negligible marginal cost, and it will give Walley, $200 in NPV terms (the actual price charged for cleaning is higher, but since it is several years down the road, the NPV less than that, and we assume it is equal to $200). Find the optimal price of trumpets in this case.