Question

The Metropolitan Company sells its latest product at a unit price of $8. Variable costs are estimated to be 40% of the total revenue, while fixed costs amount to $6,000 per month. How many units should the company sell per month in order to break even, assuming that it can sell up to 5,000 units per month at the planned price? ___units

The demand for your factory-made skateboards, in weekly sales, is q = −5p + 50 if the selling price is $p. If you are selling them at that price, you can obtain q = 2p − 30 per week from the factory. At what price should you sell your skateboards so that there is neither a shortage nor a surplus? (Round your answer to the nearest cent.)

Worldwide annual sales of a certain product were approximately −11p + 1,600 million products when the wholesale price was $p. (a) If manufacturers are prepared to supply q = 11p − 800 million products per year at a wholesale price of $p, what would be the equilibrium price? (Round your answer to the nearest cent.) $(b) The actual wholesale price was projected to be $100 in the fourth quarter of 2008. Estimate the projected shortage or surplus at that price.

Answer 1

Answer 1st Part:

Contribution per unit = Unit price - Variable cost per unit = $8 - $8 * 40% = $4.80

Units the company should sell per month in order to break even = Fixed cost per month / Contribution per unit

= $6000 /4.80

= 1,250 units

Units the company should sell per month in order to break even = 1,250 units

:

Answer 2nd part :

For Sale Price (p) at which there is neither a shortage nor a surplus:

Demand = Supply

−5p + 50 = 2p − 30

=>7p = 80

=> p = 80/7 = $11.42857

Sale Price at which there is neither a shortage nor a surplus = $11.43

Answer 3rd part:

At equilibrium price (p)

Demand = Supply

=> −11p + 1,600 = 11p − 800

=> 22 p = 2400

=> p = 2400 / 22 = $109.090909

Equilibrium price = $109.09

Annual sales = −11p + 1,600 million products

Annual supply = 11p − 800 million products

At price of $100:

Quarter sales = (-11 *100 + 1600) * 1/4 = 125 million products

Quarter supply = (11*100 − 800) * 1/4 = 75 million products

Expected shortage = 125 -75 = 50 million products

Expected shortage = 50 million products