Consider the perfectly competitive market for an "experience" good - one whose quality cannot be determined until after purchase. This good can be high quality, q = h, or low quality, q = l. Each of the price taking firms in this competitive industry have the following cost functions, depending on whether they produce high or low quality: the cost of producing low quality is C(l, x) = 7.5x+3x^2+ 27, while the cost of producing high quality is C(h, x) = 15x+3x^2+ 75, where x is the firm's output.

1. Introduce a discount factor, = .9, which gives the present value of $1.00 received one period from now. Let the market last an infinite number of periods. Suppose we wish high quality production to arise in equilibrium. Determine the minimum price premium which must be used to ensure firms will not cheat. Explain your work.

2. Solve for the price premium associated with = .75, and = .5.

3. Explain why these price premia differ.