In: Economics
Question: Your firm wants to know its long term prospects. What will be the price and quantity charged in the market long run? Explain this result and then graph the AC, MC, MR, AR and firm supply curve.
In this case, firm faces variable cost = 20q2, fixed cost=$500 and price=$240 so total cost (TC)= 20q2+500 .
Since firm is a competitive firm in long run it produces at the level where Price(P)=Marginal cost(MC). In long run due to free entry and exit in the competitive market, competition push the price level down and firm would charge prices that just equates to marginal cost of firm ( at point where MC curve cuts average cost curve from below). In long run competitive firms earn zero profits as all firms are selling homogenous product at given price and there is no barrier to entry of new firms. Thus perfect competition reduces cost to lowest of average cost incurred in long run.
Now, to equate P=MC, it is required to find MC.
Since, marginal cost is derivative of total cost i.e. MC= . It requires to derivate TC with respect to quantity
Thus, MC= 40q
Using P=MC equilibrium condition in long run where P= $240 and MC= 40q
P=MC
240=40q
q=6
Thus, a competitive firm in long run equilibrium will produce total output of 6 units at price $240 per unit
The below diagram shows Marginal cost curve cuts average cost (AC) at the lowest point of AC corresponds to this point P=$240 and quantity is 6 units. The rising portion of MC curve is the firm's supply curve.
Marginal revenue (MR) is the revenue earned from selling one extra unit in the market and in competitive market each unit is sold at given prices thus MR is same as price. Also average revenue is the revenue earned per unit i.e. AR= (price x quantity)/ quantity hence AR is prices for each unit level. In competitive market each good is sold at same price thus AR=P. Hence the condition is P, MR and AR are same under perfect competition.