Suppose a firm is a monopolist (that means only one firm supplying everything). The inverse demand function faced by the firm is given by P(Q) = 110 2Q where P(Q) is the price when a quantity Q is produced. The total cost function C(Q) required to produce Q units is C(Q) = 100 + 10Q + 1/2 Q^2 The maximum number of units that the firm can produce is 100.

a) Find the optimal price (first box) and number of products (second box) produced by the firm.

b) Next assume that the firm is a small firm. This means it will not be able to change the total market price of the product, which is now fixed at P = 80. Find the optimal number of units (third box) produced by the small firm.

c) Solve the small firm problem again if the price is P = 110. (fourth box)