Question: [Requires calculus] Again our seller starts with demand Q = 12 - P and marginal production costs of $4 per unit. The seller's transaction cost is $1 per unit, and buyers' are $2 per unit.

a. Show that profit-maximizing output is 2.5 units per year and that buyers incur costs of $9.50 per unit, of which the seller receives $7.50. Then show that profit is $6.25.

b. Now assume that the seller can reduce the buyers' transaction costs to zero by incurring an added marginal cost of $1 per unit. Show that the new profitmaximizing output is 3 units, price is $9, and profit is $9.

c. Calculate the annual consumer and producer benefits before and after.