Question

Each firm in a competitive market has a cost function of C = 10g - 492 +93 There are an unlimited number of potential firms in this market. The market demand function is Q = 30 - p. Determine the long-run equilibrium price, quantity per firm, market quantity, and number of firms. The long-run equilibrium price is $ (Enter your response as a whole number) The market quantity is units. (Enter your response as a whole number.) The number of firms is (Enter your response as a whole number) How do these variables change if a tax of $2 per unit is collected from each firm? The long-run equilibrium price is $ (Enter your response as a whole number) The market quantity is units. (Enter your response as a whole number) The number of firms is (Enter your response as a whole number)

Answer 1

Answer:

Given that:

Each firm in a competative market has a cost function of

C=10q-4q2+q3

Q=30-p

$\rightarrow$ AC=10-4q+q2

$\rightarrow$ d(AC) / dq = 2q-4 = -4 / 2 = -2

$\rightarrow$ d2(AC) / dq = -4

at q= -4

AC is minimum

AC = 10-4q+q2

= 10-4(-4)+(-4)2

=10+16+16

P =42

So,in the LR each firm will produce q=-4

So, the total industry production P=42

Q =30-p

= 30-42

=-8

n is the number of firms  

n*q=Q

n = Q / q

= -8 / -4

=2

if the tax of $2 per unit is imposed

new AC function is given by

AC = 12-4q+q2

at q=-4 , p=(min(AC)) = 44

So,in the LR firm will produce q= -4

So, total industry production at = 44 is Q= 30-44 =-14

Number of firms= n / q =Q

n =Q /q

= -14/-4

= 3.5

So, here q will remain same but industry output =Q ,industry price = p and no of firms = n will change.