Question

1. Consider Champion Manufacturing’s pricing problem for a new project: Suppose it has
estimated its total fixed costs (costs of renting land, maintenance of facilities etc.) at $30,000. Its
variable unit cost (costs of raw material, labor going into producing each unit of Champion’s
products) is estimated to be $60 per unit.
(a) Suppose Champion estimates demand for its product to be 1000 units. It decides to
implement a 5% mark-up when deciding on the price per unit of its product. Calculate the
price per unit.
(b) Using the price per unit obtained in (a), derive the break-even quantity that Champion
Manufacturing needs to sell. Comparing to the estimated demand in (a), would you say the
mark-up that Champion used above makes the new project profitable or not?

Answer 1

We have the total fixed costs = $30,000 and the variable unit cost = $60 per unit. This makes the cost function C(Q) = 30,000 + 60Q. This gives AC or per unit cost = 30000/Q + 60.

(a) Estimated demand is Qe = 1000 units. There is a 5% mark-up. Use the following formula for mark up

Mark up% = price – average cost / price

5% = (P – 30000/Q – 60)/P

5% = (P – 90)/P

This gives P – 90 = 0.05P

P* = $94.74 (approximately)

(b) Find the break-even quantity that Champion Manufacturing needs to sell where this implies TR = TC or AC = P.

94.74 = (30000 + 60Q)/Q

94.74Q – 60Q = 30000

Q(break-even) = 864 units.

c) Comparing to the estimated demand of 1000 units, the mark-up that Champion used above makes the new project profitable because the break-even quantity is lower is than the estimate demand. At Q = 1000, revenue will be $94.74*1000 = $94,740 while cost is $30000 + 60*1000 = $90000. Hence there is a profit of $4,740.