Question

General Cereals Inc. sells Crunchy-Flakies cereal. The daily demand for Crunchy-Flakies is

P= 10 - (.01 * Q)

Where P is the retail price ($) that General Cereals charges for each box of Crunchy-Flakies, and Q is the quantity of boxes of Crunchy-Flakies demanded per day.

Total variable costs per day ($) as a function of daily volume (Q) is

TVC = 2* Q

Daily total fixed costs ($) for the Crunchy-Flakies plant is

TFC = 1500

1) What price should General Cereals charge for a box of Crunchy-Flakies? What quantity will be purchased? Explain, using Excel (with or without Solver) or calculus.

2) What will be the dollar value of total revenue, total cost, and total profit? Show your work.

3) What, if any, are the effects on the optimal price, quantity, and total profit if the total fixed cost decreases? Explain, using marginal analysis.

Answer 1

Since TVC = 2Q, Marginal cost (= Average variable cost) = TVC / Q = 2

(1) Profit is maximized when Marginal revenue (MR) equals MC.

P = 10 - 0.01Q

Total revenue (TR) = P x Q = 10Q - 0.01Q²

MR = dTR/dQ = 10 - 0.02Q

Equating with MC,

10 - 0.02Q = 2

0.02Q = 8

Q = 400

P = 10 - (0.01 x 400) = 10 - 4 = $6

(2)

TR = $6 x 400 = $2400

TC ($) = TFC + TVC = 1500 + (2 x 400) = 1500 + 800 = 2300

Profit ($) = TR - TC = 2400 - 2300 = 100

(3)

Since profit is maximized by equating MR & MC, and decrease in TFC does not impact MC, lower FC will not change equilibrium price, quantity or total revenue. However, profit will decrease by the amount of fall in TFC.