assume a profit maximizing firms shortrun cost is TC 700 60

assume a profit maximizing firm\'s short-run cost is TC= 700 + 60Q. if its demand curve is P=300 - 15P compute the total revenue

Solution

Short-run total cost function is as follows -

TC = 700 + 60Q

Calculate Marginal Cost -

MC = dTC/dQ = d(700 + 60Q)/dQ = 60

Demand function is as follows -

P = 300 - 15Q

Calculate Total revenue -

TR = P * Q = (300 - 15Q) * Q = 300Q - 15Q²    ----equation (i)

Calculate Marginal Revenue -

MR = dTR/dQ = d(300Q - 15Q²)/dQ = 300 - 30Q

Being a profit maximizing firm, it will produce that level of output at which MR equals MC.

Calculating profit - maximzing output equating MR and MC

MC = MR

60Q = 300 - 30Q

90Q = 300

Q = 300/90

Q = 3.33

Putting value of Q in equation (i) to ascertain Total Revenue

TR = 300Q - 15Q² = (300 * 3.33) - [15 * (3.33)² ] = 999 - 166.33 = $832.67

The Total Revenue of firm is $832.67.