Question

Suppose the doll company American Girl has an inverse demand curve of P = 150 – 0.25Q, where Q measures the quantity of dolls per day and P is the price per doll. The marginal cost is given by MC = 10 + 0.50Q. What is the total surplus at the profit-maximizing output level? $12,250 $144,000 $4,500 $18,120

Answer 1

Answer:

$12,250

Explanation:

The profit-maximizing output is at MC = MR

We are given with Marginal Cost we need to find Marginal Revenue

MR = additional revenue for an additional unit

P = 150 – 0.25Q

Q = (150 - P)/0.25 = 600 - 4P

Total Revenue= P x Q = (150 - 0.25Q)Q

TR = 150Q-0.25Q^2

MR = will be the slope of the total revenue function:

dTR/dQ -0.5Q + 150

Now we equalize MR and MC

-0.5Q + 150 = 10 + 0.5Q

Q = 140

P when Q = 140

P = 150 - 0.25 Q = 150 - 0.25(140) = 150 - 35 = 115

Producer surplus:(using marginal cost)

$\int\limits^{140}_0 {10 + 0.50q} \, dq$

(P(140) - P(0)) x Q140

(80 - 10 ) x 140 = 9,800

Consumer surplus:

(P0 - Pm ) x Qm /2

(150 - 115) x 140 / 2 = 2.450‬

Total Surplus:  9,800 + 2,450 = 12,250