Answer:
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.