Question

Assume that fixed costs are 120 and the variable costs are 3Q per unit. a) Write down expressions for TC, AC, and MC b) Find the value of Q which minimizes AC. a) TC = (Simplify your answer. Type an expression using Q as the variable.) AC=1 (Simplify your answer. Type an expression using Q as the variable.) MC=17 (Simplify your answer. Type an expression using Q as the variable.) b) Q = (Use square root sign, integers or fractions.) Enter any number or expression in each of the edit fields.

Answer 1

A) TC = Total fixed cost + Total variable cost

Variable cost is 3Q per unit. Therefore, TVC = 3Q²

Or, TC = 120 + 3Q²

AC = (TC/Q) = (120/Q) + 3Q

MC = d(TC)/dQ = 6Q

B) when AC is minimized, d(AC)/dQ = 0

Or, -(120/Q²) + 3 = 0

Or, 120/Q² = 3

Or, Q² = 40

Or, Q = √40