Final answer:
The profit for a private seller with a demand function P = -1.2Q + 105, fixed cost of $100, and variable cost VC = 13Q + 0.013Q^2 is found by calculating total revenue, total cost, and subtracting the total cost from total revenue. To find the profit-maximizing quantity, set the marginal revenue equal to the marginal cost and solve for Q.
Step-by-step explanation:
Calculating Profit for a Private Seller
To calculate the profit for a private seller with a given demand function and costs, we need to follow certain steps. The demand function given is P = -1.2Q + 105, where P is the price at which the goods are sold and Q is the quantity sold. The fixed cost is provided as $100 and the variable cost is VC = 13Q + 0.013Q^2.
First, we need to determine the revenue, which is Total Revenue (TR) = Price (P) × Quantity (Q). The revenue function can be obtained by substituting the demand function into this equation, resulting in TR = (-1.2Q + 105) × Q.
Next, we calculate the total cost, which is the sum of fixed cost and variable cost: Total Cost (TC) = Fixed Cost + Variable Cost or TC = 100 + 13Q + 0.013Q^2.
To find the profit, we subtract the total cost from total revenue: Profit = TR - TC. By solving the equations for TR and TC and then subtracting the total cost from total revenue, we find the profit.
To determine the profit-maximizing quantity, we can set the marginal revenue equal to the marginal cost, but the specific quantity and profit value require solving the resulting equation.