Question

Suppose a profit-maximizing firm can effectively engage in second-degree price discrimination and is the only firm present in this market. The firm wishes to (and successfully does) impose a block tariff that consists of three separate blocks. The inverse market demand curve is given by P = a − bQ. The firm’s total cost curve is T C = f + cQ.

The firm’s profit-maximizing total quantity sold?

Answer 1

In a situation where the block pricing is applied where economies of scale can be realised. here we can see from the cost equation, that the marginal cost function MR=d/dQ of TC=c is constant. hence we can say that there is no diseconomies of scale as the marginal cost won't rise at all.

hence the firm can charge three different prices where two is above the marginal cost and hence average cost and the third block will be priced at the average cost level. because beyond that they will lose.

hence they will set the third block price at , P=AC

hence where P=AC, that amount of quantity is the profit maximising quantity.

Hence, a-bQ*=(f+cQ*)/Q*

or, a-bQ*=f/Q*+c

or, aQ*-bQ*²=f+cQ*

or, bQ*²+(c-a)Q*+f=0

hence solving for Q*=[-c+a+root {(c-a)²-4fb}]/2b ,[-c+a-root {(c-a)²-4fb}]/2b

Please give a thumbs up to the answer.

I made a mistake first by taking total cost In the place of average cost. If possible remove the thumbs down please.