Question

A perfectly competitive fir has the following cost function:

1/3q³-9/2𝑞² +10𝑞+500 32

and demand and supply functions are also given as:

𝑄𝐷 =50−3𝑃 and 𝑄𝑆 =10+2𝑃

What is the equilibrium price and quantity in this market?

What is the profit maximizing quantity that this firm would produce?

Answer 1

$QD = 50-3P$

$QS= 10 + 2P$

In finding Equilibrium price, 

$QS = QD$

$50 -3P= 10+2P$

$50-10 = 2P + 3P$

$40 = 5P$

$P = 40/5$

$P = 8$

ii) $Equilibrium quantity$

In finding Equilibrium quantity we use the QD equation

$QD = 50-3P$

$= 50-3(8)$

$= 50-24$

$Equilibrium quantity = 26$

2). Profit Maximizing quantity

$P = MC$

$P = 8$

$MC = dTC/dQ$

$1/3q^3 -9/2q^2 +10q +50032$

$3/3q^2 +18/2q+10$

$= 1/q^2 + 9/q +10$

$MC = 2/q+ 9$

$= 2/q + 9$

$8 = 2/q+ 9$

$2/q= 9-8$

$2/q = 1$

$q = 2$

$Profit Maximizing quantity = 2$