Final answer:
Marginal revenue is calculated as the change in total revenue divided by the change in quantity sold. To find the marginal revenue for the 251st unit, we first need to calculate total revenue at 250 and 251 units and then find the difference.
Step-by-step explanation:
To calculate the marginal revenue for the 251st unit using the demand equation Q = 778 - 21(P), we need to determine the total revenue for selling 250 units and the total revenue for selling 251 units. Marginal revenue is the change in total revenue from selling one additional unit.
First, we find the price at which 250 units are sold by plugging Q = 250 into the demand equation: 250 = 778 - 21(P). Solving for P gives us a price of P = (778 - 250) / 21. Similarly, to find the price for 251 units, we use Q = 251.
Next, calculate total revenue (TR) by multiplying the quantity sold (Q) by the price (P) for both the 250th and 251st units. Once we have both TR values, the marginal revenue (MR) is found by subtracting the TR at 250 units from the TR at 251 units.
The given variable cost does not explicitly factor into the calculation of marginal revenue as MR is concerned with revenue, not cost. However, knowing variable costs could help calculate marginal profit by subtracting marginal cost from marginal revenue.