# Optimal production level for a typical firm in long-run

Assuming all firms have identical cost functions. Now suppose there is an increasing shift in the demand curve. As we all know that for increasing costs case, both average costs (AC) and marginal costs (MC) faced by a typical firm would be higher. The question is, whether the optimal production level of a typical firm remains constant or increases (or decreases! is it possible?) as compared to previous long-run equilibrium position?

In other words, as both MC and AC curve will shift upward, can one predict with certainty the direction in which optimal production level moves to ensure MC=AC_min?

It appears we start at long-run equilibrium point.

The fact that all firms operate at the level where $q^*:MC = \min AC$, means that given demand $Q^d$ and the cost structure, what is endogenously determined is the number of firms $m$:

$$Q^d = mq^* \implies m^* = \frac {Q^d}{q^*}$$

Assume that aggregate demand increases. In the microeconomic setting we are examining things here, the cost/technology structure will not be affected by this change (we do not place bounds and the production inputs available). So in the new equilibrium, each individual firm will produce exactly the same as before.

What will change is the number of firms, which will increase, in order to accommodate the new higher required output.

• I disagree with "the cost/technology structure will not be affected by this change". As in short run, firms will earn positive economic profit, attracting new firms. The entry of new firms will drive up the production costs (both MC & AC). How can one be certain that intersection of MC and AC curve will only shift upward? – Akash Malhotra Apr 1 '17 at 21:24
• @Akash Why "the entry of new firms will drive up the production costs?" Where do you base this assertion? – Alecos Papadopoulos Apr 1 '17 at 21:32
• As mentioned in the question, "for increasing costs case", which implies entry of new firms raises the costs of production for all firms. Possible Reasons: New and existing firms may compete for scarce inputs, thus driving up their prices. New firms may impose ‘‘external costs’’ on existing firms (and on themselves) in the form of air or water pollution. – Akash Malhotra Apr 2 '17 at 18:39
• And, I think you are seeing this as Ricardian rent problem where firms with different cost functions exist (Low-high). But if all firms have identical cost functions then AC of every firm would rise. – Akash Malhotra Apr 2 '17 at 18:47