Question

Please answer part 1.

The market for fabric has only one producer. Assume that daily market demand for fabric is y = 100,000 - 100p, where y denotes the quantity and p denotes the unit price. Also assume that producing y units of fabric costs 100y.

1. How many units of fabric should the producer produce and sell in order to maximize profits? Calculate the profit-maximizing price and the profit.

2. Now suppose that to produce one unit of fabric the producer needs to use one unit of an input, cotton. There is a single producer of cotton with a cost function c(x) = 100x where x is the quantity of cotton produced. (a) Suppose that the fabric producer purchases cotton at a price q. Calculate the equilibrium quantity of cloth as a function of q. (b) How many units of cotton should the input producer produce and sell in order to maximize its profits? How many units of fabric will be sold in the market? Calculate the equilibrium prices of cotton and fabric as well as the profits of both producers. How does the output of fabric compare to part (1)?

Answer 1