Long run equilibrium price under perfect competition

I have a problem related to Ricardian rent.

I have one firm, let's call it X firm, and all of the other firms in the market. All firms have to pay some transportation costs due to their land except for X firm.

I also know that their cost functions are first degree polynomials, meaning that their marginal cost and average cost is equal to a constant number(Different than each other of course as X firm doesn't have to pay any transportation costs.)

How can I obtain the equilibrium price using only this data? I couldn't evaluate the single firm's affect on the price, does it have any influence over the price?

• Based on your studies of equilibrium, do you have any notions that could be applied here, and have you tried any of them? (This seems like a fairly straightforward exercise.) May 17, 2021 at 8:27
• In general, to find equilibrium, I solve it by equalizing demand function to the supply function. In the perfectly competitive markets, only knowing the costs functions is enough to determine the market price. We add supply curves of the firms horizontally to obtain equilibrium. However, the fact that firms have constant and different cost functions got me confused. Cost function for X is 150q, for the rest of the firms is 155q. AC=MC=Supply curve for firm X is 150, and fot rest of the firms it is 155. Would be very glad if you could give further tips. May 17, 2021 at 9:09
• From the cost functions, you should be able to tell for any price $p$ what quantity each company is willing to supply. (Are there capacity constraints?) It could be that a company is indifferent between supplying several different output levels; this happens when pricing is at cost. The question is, is there a price level at which the supply could equal demand? May 17, 2021 at 9:17
• If for individual firms the marginal and average costs are equal to each other and constant, then the lowest cost firm can take the whole market, charging marginally less than the marginal cost of the second-lowest-cost firm. The difference between this an the lowest-cost firm's cost is the rent May 17, 2021 at 14:27
• @Henry So, at equilibrium, would market price be the same as the second-lowest-cost firm's cost? May 17, 2021 at 15:49