Question

a. The ABC company is producing an item at a unit cost of $4. If the supply function is q= 160+8p, where q represents quantity produced and p represents the market price, then

i. Find the total cost function in terms of p

ii. What is the market price at which the company realizes a total profit of $500?

Answer 1

i. The total cost function in terms of p is:

$TC=Unit Costs×Q$

$TC=4×(160+8p)=640+32p$

ii. In order to find market price we have to solve the equation:

$160p+8p^2-640-32p=500$

$8p^2+128p-1140=0$

$D=128×128-4×8×(-1140)=52864$

p1= -22.37 (the price can't be negative)

p2=6.37 - the market price at which the company has the profit of $500.