The question is as follows:
The inverse market demand for provision of gas services is given by p(y) = 1/(1+y), where p is the unit price and y measures output in appropriately scaled units. Suppose the technology of gas provision is summarized by the total cost curve C(yi) = (10^−2)yi, where yi represents the units produced by firm i. Suppose all firms have access to the same technology. What is the long run competitive equilibrium of this market? Specify output exchanged, equilibrium price, number of active firms in the market, and profits of each of them.
My attempt at a solution:
I know that for a competitive equilibrium market in the long run, profit is 0. Thus, I can write 0 = p(y)*y - C(yi)y. I also know that P = MC.
Solving either gives P = 1/100 and y = 99. My question is, is this y for each individual firm or total output in the market? I am thinking it is the former since supply should be infinitely elastic at the optimal price in a competitive equilibrium. But I am stuck on solving for the number of active firms are in the market. How do I go about doing this? Thanks.