Let the inverse demand function for a single product be p(y) =- y +18

Consider a firm offering the single product with a cost function, C(y) - F+ m y where the Fixed Cost, F= 39, and the marginal cost, m =2 (Recall producer surplus-producer profit). Now consider three pricing schemes:

(i) Scheme 1 : Let m1 be the lowest uniform price that allows the firm to break even

Let y1 be the demand at this price Compute m and y1, and the consumer and producer surpluses

(ii) Scheme 2 The nonlinear pricing scheme is consumer's payments= m1 y if y < y1

= m1y1 + m2 (y-y1) if y1

Denote by y2 the total demand for this scheme. Compute y2, and the consumer and producer surpluses

(iii) Scheme 3 The nonlinear pricing scheme is (recall m=2) consumer's payments = m1 y if y < y1

=m1y1 + m2 (y-y1) if y1

= m1y1 + m2 (y2-y1) + m (y-y2). if y2

For this scheme, compute y3, the total demand, and consumer & producer surpluses