Question

assume that the pickle industry is perfectly competitive and has 250 producers. two hundred of these producers are high cost producers, each with a short run supply curve given by Qhc = 2P. fifty of these producers are low cost producers, with a short run supply curve given by Qlc= 4P. quantities are measured in jars and prices are dollars per jar.

a) derive short run industry supply curve for pickles

b) if the market demand curve for jars of pickles is given by Q^D = 8000 - 200P, what are the market equilibrium price and quantity of pickles?

c) AT THE PRICE you found in part (b), how many pickles does each high cost firm produce? each low cost firm?

d) at the price you found in part (b), determine the industry producer surplus.

Answer 1

Solution:

a) According to what's given:

At some particular price P, each "high type (HT)" producer (total of 200 such producers) supplies 2P, and each "low type (LT)" producer (50 such producers) supplies 4P, in the short-run. So, short run industry supply curve for pickles for all producers together becomes:

Q(P) = 200*2P + 50*4P

Q(P) = 400P + 200P = 600P

b) Given the market demand curve: Qd = 8000 - 200P

We already found in above part, the market supply curve as: Qs = 600P

Equilibrium occurs where the market demand equals the market supply curve, that is, Qd = Qs

8000 - 200P = 600P

8000 = 800P

So, P = 8000/800 = $10 per jar

Then, equilibrium quantity can be found by substituting in either of market demand or supply function:

Q = 600*10 = 6,000 pickle jars

Thus, market equilibrium quantity is 6,000 pickle jars and equilibrium price is $10 per jar.

c) At price, P = $10, each high-cost firm producer produces Qhc = 2*10 = 20 pickle jars.

At this price, a low-cost firm producer produces Qlc = 4*10 = 40 pickle jars.

d) Industry producer surplus is the gain for producers, and is denoted by the area lying between the supply curve and equilibrium price. (Note that it is a triangular area as the supply curve is linear) So, area of triangle = (1/2)*base*height

Since, the supply curve starts from the origin, the height will equal the equilibrium price itself, so

Producer surplus = (1/2)*Q*P

Producer Surplus = (1/2)*6000*10 = $30,000

So, industry producer surplus is $30,000.