Final answer:
The marginal revenue of the 25th unit for a monopolist using the demand equation MWTP(Q) = 120 - 4Q is -80. This is calculated by deriving the marginal revenue function from the total revenue, which is twice the slope of the demand curve, resulting in MR = 120 - 8Q.
Step-by-step explanation:
The student is asking how to calculate the marginal revenue of the 25th unit for a monopolist's demand curve represented by the equation MWTP(Q) = 120 - 4Q. To find the marginal revenue, one must understand the relationship between total revenue and quantity sold. Marginal Revenue (MR) is the additional revenue that one more unit of the good would bring in. It's calculated as the change in total revenue divided by the change in quantity (MR = ∆TR/∆Q).
Steps to Calculate Marginal Revenue:
Understand the demand function, which in this case is MWTP(Q) = 120 - 4Q.
Derive the Total Revenue (TR) by multiplying the price (P) times the quantity (Q).
Derive the Marginal Revenue function by taking the derivative of the Total Revenue with respect to quantity (Q).
Substitute the given quantity into the Marginal Revenue function to find the marginal revenue for that specific unit. In this case, substitute Q=25 to find MR for the 25th unit.
Given that the demand function is linear, the marginal revenue function will have twice the slope of the demand curve. Therefore, MR = 120 - 8Q. To find MR at Q=25, substitute 25 for Q in the MR function:
MR at Q=25 = 120 - 8(25) = 120 - 200 = -80.
The marginal revenue of the 25th unit is -80. This indicates that if the monopolist sells the 25th unit, the total revenue would decrease, a characteristic of a monopolist's revenue structure when the quantity sold is high.