Final answer:
a. The total revenue from selling 500 units is $55,000. b. The marginal revenue at 500 units is -$0.1. c. More revenue is expected from the 501st unit sold compared to the 701st.
Step-by-step explanation:
a. To find the total revenue from the sale of 500 units, we substitute x = 500 into the demand function p = 160 - 0.1x. Hence, p = 160 - 0.1(500) = 160 - 50 = $110. The total revenue is calculated by multiplying the quantity sold (500 units) by the price ($110). Therefore, the total revenue from the sale of 500 units is $55,000.
b. The marginal revenue represents the additional revenue generated from selling one more unit. To find the marginal revenue at 500 units, we first need to find the revenue from selling 500 units and then the revenue from selling 501 units. The revenue from selling 500 units is $55,000 (which we calculated in part a). The revenue from selling 501 units can be found by substituting x = 501 into the demand function: p = 160 - 0.1x. Hence, p = 160 - 0.1(501) = 160 - 50.1 = $109.9.
The marginal revenue is then calculated by taking the difference in revenue between selling 501 units and selling 500 units: Marginal revenue = Revenue from selling 501 units - Revenue from selling 500 units = $109.9 - $110 = -$0.1. The interpretation of the negative marginal revenue is that the firm is experiencing diminishing returns, where revenue decreases with each additional unit sold.
c. Since the marginal revenue at 501 units is negative, it means that selling an additional unit will result in a decrease in total revenue. Therefore, more revenue is expected from the 501st unit sold compared to the 701st unit.