Question

Suppose you are a perfectly competitive firm producing computer memory chips. Your production capacity is 1000 units per year. Your marginal cost is $10 per chip up to capacity. You have a fixed cost of $10,000 if production is positive and $0 if you shut down. What are your profit-maximizing levels of production and profit if the market price is (a) $5 per chip, (b) $15 per chip, and (c) $25 per chip? For case (b), explain why production is positive even though profits are negative.

Answer 1

$Marginal \space cost \space per \space unit = \$10$

$Total\space Quantity\space = 1000$

$Total\space Fixed\space Cost = \$10,000$

Working.

a)

$Market\space price = \$5$

$Total \space Revenue = \$5 \times 1,000 = \$5,000$

$Total\space Cost = Total\space Fixed\space Cost\space + \space Total\space Variable\space Cost$

$Total \space Cost = \$10,000 + {1000 \times \$10} = \$20,000$

Profit = Total Revenue - Total cost

$Profit = \$5,000 - \$20,000 = - \$15,000$

b)

Market Price $= \$15$

$Total\space Revenue = \$15 \times 1,000 = \$15,000$

$Total \space Cost = Total\space Fixed\space Cost + Total\space Variable\space Cost$

$Total \space Cost = \$10,000 + {1000 \times \$10} = \$20,000$

$Profit = Total \space Revenue - Total\space Costs$

$Profit = \$15,000 - \$20,000 = - \$5,000$

Since the market price is higher, firms are willing to supply more goods than the demand hence leading to excess supply.

c)

Market Price $= \$25$

$Total \space Revenue = \$25 \times 1,000 = \$25,000$

$Total\space Cost = Total \space Fixed\space Cost + Total \space Variable\space Cost$

$Total\space Cost = \$10,000 + {1000 \times \$10} = \$20,000$

$Profit = Total\space Revenue - Total \space Costs$

$Profit = \$25,000 - \$20,000 = \$5,000$