Question

For a certain product, the linear demand curve is described by the equation, Quantity = 14,000 - 539 * Price. Variable cost to manufacture this product is $10 per unit. Calculate optimal price for this product. Rounding: penny.

SHOWING HOW YOU GOT YOUR ANSWER WILL HELP THE MOST. MARKETING METRICS IS THE SUBJECT OF THE QUESTION.

Answer 1

Answer : In case of linear demand curve, the equilibrium condition occurs at that point where

MR( Marginal Revenue ) = MC( Marginal Cost )

Given,Q (Quantity) = 14,000 - 539*P (Price) => 539P = 14000 - Q => P = (14000 - Q)/539

=> P = 25.974 - 0.002Q

=> TR (Total Revenue) = P * Q = (25.974 - 0.002Q)*Q = 25.974Q - 0.002Q^2

MR (Marginal Revenue) = TR / Q = 25.974 - 0.004Q

Variable cost = $10 per unit, Total variable cost = 10Q [ As total quantity level is Q ]

As MC is related to variable cost only, let total fixed cost is K (constant).

Now TC ( Total Cost ) =Total Variable cost + Total Fixed cost = 10Q + K

MC = TC / Q = 10

At equilibrium MR = MC

=> 25.974 - 0.004Q = 10

=> 25.974 - 10 = 0.004Q

=> 15.974 / 0.004 = Q

=> Q = 3993.5

Now, P = 25.974 - 0.002 * 3993.5 = 17.987 = 18

Therefore, the optimal price level is $18.