Anthonyâs Bees is an Internet e-tailer that sells equipment to aspiring beekeepers. A complete starter kit in this competitive market sells for $900. Anthonyâs total costs are given by TC=3ð3 , where Q is the number of starter kits he sells each month. The corresponding marginal cost of producing beehives is ðC=9ð2 . Required:
a. What is Anthony's marginal revenue from selling another starter kit?
b. How many starter kits should Anthony sell each year in order to maximize his profits?
c. How much profit will Anthony earn at this output level?
d. Suppose Anthony is producing the quantity indicated in part b. If he decides to produce one more starter kit, what will his new profit be?

a. $900

b. 10 starter kits

c. $6,000

d. $5,907

Explanation:

The following are correctly stated first before answering the questions:

P = Price = $900

TC = Total cost = 3Q^3

ðC = Marginal cost = 9Q^2

a. What is Anthony's marginal revenue from selling another starter kit?

Since a complete starter kit sells for $900, Anthony's marginal revenue from selling another starter kit is therefore equal to $900 for a complete starter kit.

Therefore, we have:

MR = Marginal revenue = P = $900

b. How many starter kits should Anthony sell each year in order to maximize his profits?

In theory of firm in economics, profit is maximized when MC = MR. Since,

MC = 9Q^2

MR = 900

We have:

9Q^2 = 900

Q^2 = 900 / 9

Q^2 = 100

Q = 10

Therefore, Anthony should sell 10 starter kits in order to maximize his profits.

c. How much profit will Anthony earn at this output level?

Total revenue = TR = P * Q

Since,

P = $900

Q = 10

We have:

TR = $900 * 10 = $9,000

TC = 3Q^3

Substituting for Q, we have:

TC = 3 * 10^3 = 3 * 1,000 = $3,000

Profit = TR - TC = $9,000 - $3,000 = $6,000

Therefore, the amount of profit Anthony earn at 10 output level (by selling 10 starter kits) is $6,000.

d. Suppose Anthony is producing the quantity indicated in part b. If he decides to produce one more starter kit, what will his new profit be?

By producing one more starter kit, we will have:

New Q = 10 + 1 = 11

Therefore, we have:

New TR = $900 * 11 = $9,900

New TC = 3 * 11^3 = 3 * 1,331 = $3,993

New profit = New TR - New TC = $9,900 - $3,993 = $5,907

Therefore, the amount of new profit will be $5,907 if Anthony decides to produce one more starter kit.

Additional Note:

The part d. above shows that producing 11 stater kits which is one more starter kit greater than the profit maximizing 10 starter kit will make profit to fall from $6,000 to $5,907. It is therefore better for Anthony to continue to produce 10 starter kits in order to continue to maximize profit. Because, if he should produce more or less than 10, his profit will fall.

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