Question

Assume there are exactly two consumers, person H and person L, and let VH(q) = 5q and VL(q) = 4q. (Note that at least one of our usual assumptions on V is violated…which one(s)?) Assume the total cost of producing one high quality good and the low quality good is C(qH) = qH2 /2 and C(qL) = qL 2 /2 respectively. Note that marginal value of q is just 5 to the H type and 4 to the low type. Costs are MCH = qH and MCL = qL.)

a.) Assuming the monopolist can observe the type of any given consumer, set up the monopolist’s profit function with relevant constraints and solve this function for the profit maximizing quantities and total package prices (qL,RL) and (qH,RH).

b.)Assuming the monopolist cannot observe the type of any given consumer, set up and solve monopolist’s profit function with relevant constraints

Answer 1

Answer:-

The following problem relates to a monopolist who faces two types of consumers. The first type prefers a high quality product and the other type prefers to compromise with a low quality product. The first one is categorised as a High Type (H) and the other as a Low Type (L).

Moreover, in this problem a basic law of a monopolist is violated where the TR curve is a straight line shooting out from the origin in the 1st quadrant which is impossible because the curve must be a logarithmic curve and not a linear curve.

The aforesaid curve is not possible for a monopolist and is possible only in case of a perfect competitor.

a)

For High Type:-

For Low Type:-

Profit maximising package price for H type

Profit maximising package price for L type =

b)

Let the probability of H type be 'a' and of L type be 'b';

where 0<a,b<1.

Eqauls the Equation(i) and (ii), we get,

Profit maximising package price for H type =

Profit maximising package price for L type =

.