Final answer:
To determine the ideal volume of production, calculate the Marginal Revenue (MR) and Marginal Cost (MC) from the Total Revenue (TR) and Total Cost (TC) equations and find where MR equals MC. Calculus can be used to derive these functions and determine the profit-maximizing quantity for the private seller.
Step-by-step explanation:
The ideal volume of production for the private seller with the given demand function P = -1.0Q + 108 and the variable cost function VC = 10Q + 0.014Q2, with a fixed cost of 100, is determined by maximizing profit, which is total revenue minus total cost. Total Revenue (TR) is calculated by multiplying the price (P) by the quantity (Q). Given the demand function, TR = PQ. Total Cost (TC) is the sum of Fixed Cost (FC) and Variable Cost (VC), so TC = FC + VC. Profit (π) is TR - TC.
To find the profit-maximizing quantity, we should first derive the Marginal Revenue (MR) and Marginal Cost (MC) functions. MR is the derivative of TR with respect to Q, and MC is the derivative of TC with respect to Q. The profit-maximizing quantity occurs where MR = MC. We can use calculus to derive and equate these two functions, then solve for Q. Given the cost structure and functions provided, more detailed calculations with derivatives are required to arrive at the precise quantity for maximum profit. Solving Models with Graphs or using more advanced functions like MC and MR is the traditional approach for finding the optimal production volume in economics.