Question

5. N95 respirators are a form of personal protection equipment designed to filter out 95% of airborne particles and are currently in high demand. These masks are relatively homogeneous and have many suppliers Suppose that each N95 respirators producer faces identical costs of C(q) = 9+2q+g, and the market demand is Q = 26-p. (a) (16 points) What is the individual's long-run quantity produced? (b) (16 points) What is the long-run market equilibrium price and quantity? (c) (16 points) How many firms would be in this market? (d) (8 points) If the government decided to start providing a lump-sum subsidy (8), how would you expect the answers above to change?

Answer 1

Solution :

Given Information :

C(q) = 9 + 3q + q²

(a) :- Average Cost = AC = C(q)/q = (9/q) + 3 + q

Marginal Cost = MC = dC(q)/dq = 3 + 2q

In long run, a competitive firm produces an output level with the end goal that AC is minimized.

Set AC = MC to discover the output at which AC is minimized.

(9/q) + 3 + q = 3 + 2q

9/q = q

q² = 9

q = 3

In long run, a firm will produces 3 units.

(b) :- We have determined to some extent (a) that :

AC = (9/q) + 3 + q

Set q = 3 to get minimum AC

Minimum AC = (9/3) + 3 + 3 = $9

Long run price = Minimum AC = $9.

Long run quantity will be quantity demanded at the price of $9.

So, Long run quantity = Q = 21 - p = 21 - 9 = 12 units.

(c) :- Number of firms = Long run quantity produced/ Output of a firm

= 12/3 = 4 firms.

(d) :- If there should be lump sum subsidy, Average cost will decrease.

Along these lines, price will decrease in long run and higher quantity will be demanded.

Output that limits AC will likewise be lower.

Along these lines, we can say that number of firms will increase in long run with each firm having a diminished output.