Carpet, Inc. is the sole distributor of fine Oriental carpets in the area. The cost of producing and importing one carpet is $1,000. Last year, a total of 3,200 carpets were sold, at a price of $3,000 per unit. This year, Carpet, Inc. hired a consulting firm (KPMG) which estimated that elasticity of demand for carpets equals -3, and that thedemand for carpets is linear.

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

can you help Carpet, Inc. choose the optimal price? How many carpets would it sell this year?

Before Carpet, Inc. had a chance to rewrite the prices and place the order of carpets, the same consulting company did a survey and concluded thathalfof customers who buy carpet from Carpet, Inc. would use Carpet, Inc. for cleaning services (andthe other halfwould not). The cleaning service has a negligible marginal cost, and it will give Carpet, Inc. $400 in NPV terms (the actual price charged for cleaning is higher, but since it is several years down the road, the NPV is less than that, and we assume it is equal to $400). Find the optimal price of carpets in this case.