A firm faces the demand curve: P = 2,241 - 19Q. What is the firm’s revenue maximizing price? Enter as a value (round to two decimal places if necessary)
The demand curve is given as:
P = 2,241 - 19Q
The total revenue is the product of price and quantity. So,
TR = PQ = (2,241 - 19Q)(Q) = 2,241Q - 19Q²
The revenue is maximized by putting the marginal revenue equal to zero. So,
MR = d(TR)/dQ = 2,241 - 38Q
Putting the marginal revenue equal to zero:
2,241 - 38Q = 0
38Q = 2,241
Q = 2,241/38 = 58.974
Putting Q = 58.974 in the demand function:
P = 2,241 - 19(58.974) = 1,120.50
So, the firm will charge a price of $1,120.50 (approximately) to maximize the revenue.
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