Question

The demand curve for a product is given by Q = 800 – 0.1P where P denotes price and Q denotes quantity of the product. The industry comprises large number of firms. Each firm's cost function is 

C(q) = 2000 + 500q+ 20q²

(c) Assuming that there are 20 firms in the industry. Find the industry supply function. Using industry supply and demand function find price and aggregate output in the short-run equilibrium.

Answer 1

Answer

the supply function of each firm is equal to the marginal cost function of the function

MC=change in the total cost and the change in function is found by differentiation of the TC function

Maq a (2000+ 500q + 2002) T = 500 + 409 ac() MC = 500 + 409 09

so the individual firm supply function is

P=500+40q

converting to normal form

P=500+40q

40q=P-500

q=0.025P-12.5

the market supply curve is:

Q=q*number of firms =q*20=(0.025P-12.5)*20=0.5P-250

Q=0.5P-250

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the equilibrium is at Qd=Qs

800-0.1P=0.5P-250

0.6P=1050

P=1750

Q=800-0.1*1750

Q=625

the market equilibrium quantity is 625 and price is $1750

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the indivusl finr quantity is

MC=P

500+40q=1750

40q=1250

q=31.25