Suppose you are the manager of a watch-making firm operating in a competitive market. Your cost of production is given by C = 100 + Q2, where Q is the level of output and C is total cost.
A) If the price of watches is birr 60, how many watches should you produce to maximize profit?
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To maximize profit, you need to find the level of output at which marginal revenue equals marginal cost. In this case, the marginal cost is given by the derivative of the total cost function with respect to the level of output Q, which is dC/dQ = 2Q.
To find the marginal revenue, you need to consider that in a competitive market, the price is equal to the marginal revenue. So, in this case, the marginal revenue is 60 birr.
Setting the marginal revenue equal to the marginal cost, we have 60 = 2Q.
Now, solve the equation for Q:
Q = 60/2 = 30.
Therefore, to maximize profit, you should produce 30 watches.