Suppose you are the manager of a watch producing firm in a competitive market. If your cost of production is given by TC=100+Q2
a) How many watches should you produce when the unit price of a watch is 60 Br.?
b) What is the maximum profit?
To determine the optimal production level to maximize profit, we need to use the profit formula:
Profit = Revenue - Cost
The revenue formula is given by:
Revenue = Price x Quantity
So, we can substitute the given cost and revenue formulas into the profit formula:
Profit = (Price x Quantity) - (100 + Q^2)
a) If the unit price of the watch is 60 Br., we can write the profit formula as:
Profit = (60 x Q) - (100 + Q^2)
To find the optimal production level, we need to take the derivative of the profit function with respect to Q and set it equal to zero:
dProfit/dQ = 60 - 2Q = 0
Solving for Q, we get:
Q = 30
Therefore, the optimal production level is 30 watches when the unit price is 60 Br.
b) To find the maximum profit, we can substitute Q = 30 into the profit formula:
Profit = (60 x 30) - (100 + 30^2) = 900 - 1000 = -100 Br.
This means that the maximum profit is -100 Br., which is a loss. It is not possible to make a profit in this case, given the cost function and the unit price.