To determine the total revenue made by a single price monopolist, we need to calculate the product of the quantity demanded (qd) and the price (p).
In this case, the quantity demanded (qd) is given by the equation qd = 1000 - 5p. This equation represents the relationship between the price and the quantity demanded.
To find the total revenue, we multiply the quantity demanded (qd) by the price (p). Mathematically, this can be expressed as R = qd * p.
Substituting the given equation for qd into the equation for total revenue, we have:
R = (1000 - 5p) * p
To simplify the equation, we can expand the expression:
R = 1000p - 5p^2
Now, to find the total revenue, we need to determine the value of p that maximizes this equation. This is because a monopolist wants to set the price that will yield the highest total revenue.
To find the maximum value, we can take the derivative of the equation with respect to p, and set it equal to zero:
dR/dp = 1000 - 10p = 0
Solving for p, we have:
10p = 1000
p = 100
So, the monopolist should set the price at 100.
To find the total revenue, we substitute this price back into the equation:
R = (1000 - 5(100)) * 100
R = 500 * 100
R = 50,000
Therefore, the single price monopolist would make a total revenue of 50,000.
None of the options provided (5000, 4000, 3000, 2000) match the correct answer. The correct answer is 50,000.