Answer to Question #182279 in Microeconomics for Christian Takyi Mensah

Question

The market demand for a type of carpet has been estimated as: P = 40 -

0.25Q, where P is price (GHØ/yard) and Q is rate of sales (hundreds of yards per month). The market supply is expressed as: P = 5.0 + 0.05Q. A typical firm in this market has a total cost function given as: C = 100 - 20.0q + 2.0q2.

Determine the equilibrium market output rate and price.

Determine the output rate for a typical firm.

Determine the rate of profit (or loss) earned by the typical firm

 

Answer 1

When Demand meets Supply for equilibrium Price and Quantity

$Q_d=Q_s \\ 160-4P=20P-100 \\ 260=24P$

$P_e=10.83$ Equilibrium Price

$Q_e=160-4 \times 10.83 =116.66$ Equilibrium Quantity

For Typical Firm P=MC

$10.83=4q-20 \\ 4q=30.83 \\ q=7.70$

Profit for typical firm

Profit=Revenue-Cost

$=P \times q-C \\ =10.83 \times 7.70 -100+20 \times 7.70 -2(7.70)^2=1883$