Assume there are two groups A and B of consumers in a market There is a monopoly producer in the market and the total cost of producing Q units of output is CQ=5Q² The inverse demand functions of gr

Since the monopolist can only sell to group B consumers, the market demand function is given by q_B = Q. We can rewrite the inverse demand function for group B consumers as p(Q) = 10 - Q.

The monopolist's profit is given by π(Q) = TR(Q) - TC(Q), where TR(Q) is the total revenue and TC(Q) is the total cost. Total revenue is equal to the unit price times the quantity sold, or TR(Q) = p(Q)Q. Total cost is given by C(Q) = 5Q².

To find the profit-maximizing quantity, we need to find the quantity that maximizes the monopolist's profit function. Taking the derivative of the profit function with respect to Q and setting it equal to zero, we get:

dπ(Q)/dQ = d(TR(Q))/dQ - d(TC(Q))/dQ = 10 - 10Q - 10Q = 0

Solving for Q, we get Q = 1. The monopolist should produce and sell 1 unit of output.

To find the profit-maximizing unit price, we plug Q = 1 into the inverse demand function for group B consumers:

p(Q) = 10 - Q = 10 - 1 = 9

The profit-maximizing unit price is $9.

Finally, we can calculate the optimal profit by plugging Q = 1 and p = 9 into the profit function:

π(Q) = TR(Q) - TC(Q) = p(Q)Q - C(Q) = (9)(1) - 5(1)² = $4.

The monopolist's optimal profit is $4