Question

Question 4:

The ethanol industry is perfectly competitive, and each producer has the long-run marginal cost function MC(Q)=48−24Q+3Q2MC(Q)=48−24Q+3Q2. The corresponding long-run average cost function is AC(Q)=48−12Q+Q2AC(Q)=48−12Q+Q2. The market demand curve for ethanol is QD=240−10PQD=240−10P.

What is one firm's inverse long-run supply curve with the minimum level of price for the firm to operate?

What is the optimal level of quantity produced by each firm in the long-run?

What is the long-run equilibrium price in this industry?

What is the long-run industry ((or market)) supply curve?

What is ther equilibrium quantity demanded in this market? How many active producers are in the ethanol market in a long-run competitive equilibrium?

Answer 1

Solution:-
1):- A firm's inverse long-run supply curve can be found by equatıng the price with the Marginal
Cost (MC).

Therefore, from the given MC curve,
P=MC
P = 48-24Q +30²

Therefore, the inverse long-run supply curve is,
P = 48-24Q+3Q²

2):- Since it 1s a perfectly competitive market, the firms will only be able to earn normal profits and therefore, will produce at the minımum of the Marginal Cost (MC) curve. Thus, at this point,

Average Cost (AC) and MC are equal:-

MC= AC
48-24Q +3Q² = 48-12Q+Q²
2Q =12Q
Q=6
Therefore, at optimal level, the quantity will be 6 units.

3):-
In the long run, the price is determined at the level where it is equal to MC,
P= MC
=48-24Q +3Q²
=48-24(6)+3(6)²
=48-144+108
=12
Thus, the long-run equilbrum price is $12.

4):- Thus, the long-run industry supply curve is P=12.

5):- At price of $12, the quantity demanded is:-
Qđ = 240-10P
= 240-10(12)
= 240-120
= 120
Therefore, equilibrium quantity demanded is 120 units.

Now, the active producers are
Active Users = Total quantity produced/Quantity produced by each firm

= 120/6
= 20
Thus, there are 20 active producers.