Question

A producer of felt-tip pens has received a forecast of demand of 47,000 pens for the coming month from its marketing department. Fixed costs of $29,000 per month are allocated to the felt-tip operation, and variable costs are 28 cents per pen.

A) Find the break-even quantity if pens sell for $4 each. (Round your answer to the next whole number.)
B) At what price must pens be sold to obtain a monthly profit of $17,000, assuming that estimated demand materializes?

Answer 1

The table shows the calculation of total revenue, marginal revenue, total cost, and marginal cost for each output level. The diagram of the total revenue and total cost curves and the marginal revenue and marginal cost curves are also shown. The profit maximizing quantity is determined by observing the point where marginal revenue equals marginal cost.

Step-by-step explanation:

Calculation of Total Revenue:

Quantity: 1 Price: $72 Total Revenue: $72

Quantity: 2 Price: $72 Total Revenue: $144

Quantity: 3 Price: $72 Total Revenue: $216

Quantity: 4 Price: $72 Total Revenue: $288

Quantity: 5 Price: $72 Total Revenue: $360

Calculation of Marginal Revenue:

Quantity: 1 Marginal Revenue: $72

Quantity: 2 Marginal Revenue: $72

Quantity: 3 Marginal Revenue: $72

Quantity: 4 Marginal Revenue: $72

Quantity: 5 Marginal Revenue: $72

Calculation of Total Cost:

Quantity: 1 Total Cost: $164

Quantity: 2 Total Cost: $184

Quantity: 3 Total Cost: $214

Quantity: 4 Total Cost: $284

Quantity: 5 Total Cost: $370

Calculation of Marginal Cost:

Quantity: 1 Marginal Cost: $64

Quantity: 2 Marginal Cost: $20

Quantity: 3 Marginal Cost: $30

Quantity: 4 Marginal Cost: $70

Quantity: 5 Marginal Cost: $86