Question

The market demand and supply functions for a type of carpet known as KP-7 have been estimated, respectively, as: QD =140–4P, QS =–100+20P. where P is the price (dollars per yard) and Q is the rate of sales (hundreds of yards per month). A typical firm in this market has a total cost function given as: TC = 50 – 20q + 3q2, and MC = 6q - 20 where q is the firm’s output level.

(a) What are the market price and quantity?

(b) What is the output rate of the typical firm? What is this typical firm’s profits? How many firms are in the industry? (assume all firms have the same cost functions and are identical)

(c) On two graphs, side-by-side, draw the market and individual firm curves, highlighting the price and output levels.

Answer 1

QD =140–4P, QS =–100+20P are the demand and supply functions, we know that at the point of equilibrium the quantity demanded equals the quantity supplied.

Thus 140–4P =–100+20P

240 = 24P or P = 10, at P=10 (Market Price) , market quantity will be Q = 140-4*10 = 100 (Market Quantity)

The equilibrium for firm will be P=MC

10 = 6q-20

6q = 30 or q= 5 (output of a typical firm)

ATC =TC/q, at q = 5, = 50/q-20q/q+3q^2/q

= 50/q-20+3q, at q=5, ATC = 50/5-20+3*5 = 5

Profits = (P-ATC)*q = (10-5)*5 = 25 (for a typical firm)

The number of firms (N) = Q/q = 100/5 = 20 firms