Question

A business is currently producing a = 400 units of its product per month. Assume the following is true: Its costs are C(400) = 8500, and the marginal cost is MC(400) = 10. . Its revenues are R(400) = 8800, and the marginal revenue is MR(400) = 22. (a) (6 points) Which of the following statements is true when production is at q = 400 units? (List the letters of all that apply - you do not need to explain your answers.) (A) The business is operating at a loss (i.e. profit is negative). (B) Costs increase by about $10 each month. (C) Profits increase by about $12 each month. (D) An additional unit of production per month will increase costs. (E) An additional unit of production per month will increase revenue. (F) An additional unit of production per month will increase profit. (b) (6 points) Estimate how much profits will increase or decrease if production is changed from q = 400 to q = 410. Should the business increase production if it can? (c) (6 points) A tax of $1 per unit is enacted. Is the business still profitable? Estimate the new break-even point.

Answer 1

a) Following statements are true

D,E,F

Explanation

A) False

The business is not operating at a loss. It makes a profit of $300

Sales = 8800

Costs = 8500

Profit = Sales - costs = 8800 - 8500 = $300

B) Fasle

Marginal Cost $10 means the additional cost for making one additional unit. So the soct increases by $10 for every unit additional unit of production. The increase in costs is not for a period of time (by one month).

C) False

Again profit increases by $12 for each additonal unit of production. Here we got Marginal Revenue (It is the additional revenue for each additional unit of sales) and Marginal cost (Additional cost for each additional unit of production). So extra profit is only for one extra unit of production not for a period of time.

D) True

This statement is true as additional unit of production will increase the cost of production by $10 for every additional units produced.

E) True

As the Marginal Revenue is $22, additional unit of production will increase its revenue by $12 for each and every extra units produced and sold.

F) True

This statement is also correct as additional unit of production will result in an additional revenue of $22 and additional cost of $10, which in turn will increase the profit by $12 for each additional unit of production.

b)

If the production is increased from 400 to 410 units, the profit will increase by $120.

Marginal Revenue = 22

Marginal cost = 10

Additional profit for each unit = 22 - 10 = 12 per unit

Additional units produced = 410-400 = 10 units

Total increase in profit = $12 x 10 units = $120

So they should increase the production as it will increase the profit.

c)

The business is profitable even with an increase in tax of $1 per unit. Profit will increase by $11 for every additional unit.

Marginal Revenue = 22

Marginal Cost = 10 + Tax $1 = 11

Profit per unit = $11

When the tax is increased by $1 Marginal cost will increase by $1

So the new marginal cost = $11

New contribution = Sales Revenue - Marginal Cost

= 22 - 11 = $11

Fixed cost = Total cost - Variable cost

Variable cost for making one additional unit is $10.

= 8500 - (400 x 10) = 4000

New BEP = Total Fixed cost / Contribution per unit

= 4500 / 11 = 409 units.