Question

For a certain product, Maximum Willingness to Buy is 16,788 units, while Maximum Reservation Price is $59.93. Variable cost to manufacture this product is $24.68 per unit. Calculate optimal price for this product. Rounding: penny.

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

Answer 1

Maximum reservation price is the price when quantity is zero, and maximum willingness to buy is the quatity when price is zero.

Demand function: P = a - bQ

Using given data,

When P = 0, Q = 16,788

0 = a - 16,788b..................(1)

When Q = 0, P = $59.93

59.93 = a

Substituting in (1),

0 = 59.93 - 16,788b

16,788b = 59.93

b = 0.0036

Therefore, demand function is

P = 59.93 - 0.0036Q

For a downward sloping demand function, profit is maximized when Marginal revenue (MR) equals MC (= $24.68).

Total revenue (TR) = P x Q = 59.93Q - 0.0036Q²

MR = dTR/dQ = 59.93 - 0.0072Q

Equating with MC,

59.93 - 0.0072Q = 24.68

0.0072Q = 35.25

Q = 4,895.83

P = 59.93 - (0.0036 x 4,895.83) = 59.93 - 17.63) = $42.31