Based on the table of quantity Q and marginal revenue MR at

Based on the table of quantity (Q and marginal revenue (MR), at what quantity is profit maximized? If the corresponding price for a quantity of 1 is $17, at what price is profit maximized? Assume MR and market demand are linear. Assume MC 2. MR 15 4 -1 a. 5; S9 b. 5; $8 ?. 4; $11 d. 4; $9

Solution

Option (c).

Profit is maximized when MR >= MC. From the data, closest value of MR and MC are for output level of 4 units when MR = $3 and MC = $2, so Q = 4.

Linear demand function is: P = a - bQ.

Total revenue (TR) = P x Q = aQ - bQ²

MR = dTR/dQ = a - 2bQ

From given table,

When Q = 1, MR = 15

15 = a - 2b.........(1)

When Q = 2, MR = 11

11 = a - 4b.........(2)

(1) - (2) yields: 4 = 2b

b = 2

a = 15 + 2b [From (1)] = 15 + (2 x 2) = 15 + 4 = 19

Demand function: P = 19 - 2Q

Therefore, when Q = 4, P = 19 - (2 x 4) = 19 - 8 = $11