Answer to Question #77786 in Economics for Adari sagar

Question

if p=12-3x is the demand function and A=2x is the average cost function of monopolist ,find the equilibrium output and price.find the maximum profit also

Answer 1

If p =12-3x is the demand function, then MR = TR' = (p*x)' = 12 - 6x.
If A=2x is the average cost function of monopolist, then MC = TC' = (A*x)' = 4x.
The equilibrium output is at MR = MC, so:
12 - 6x = 4x,
x = 1.2,
p = 12 - 3*1.2 = 8.4.
At equilibrium A = 2*1.2 = 2.4.
The maximum profit is:
TP = (p - A)*x = (8.4 - 2.4)*1.2 = 7.2.