Final answer:
Creating expense and revenue functions requires setting a revenue function based on price and quantity sold, and an expense function based on fixed and variable costs. The difference between explicit and implicit costs also plays a significant role in determining a firm's financial health.
Step-by-step explanation:
To model a business in terms of the price p, we can create expense and revenue functions. The revenue function is typically represented as R(p) = p × Q, where Q is the quantity sold, and the price per unit is p. This function shows that revenue is the product of the price and the quantity sold, and it changes with the demand for the firm's products. The expense, or cost function, reflects the total cost incurred by the production and selling of the goods. The total cost function can be expressed as C(Q) = F + V(Q), where F represents fixed costs, and V(Q) represents variable costs as a function of quantity Q. Fixed costs remain constant regardless of the quantity produced, while variable costs change with the level of output.
To understand a firm's profitability, we subtract the total cost from total revenue. Profitability is thus calculated as π(Q) = R(Q) - C(Q). Understanding the difference between explicit costs and implicit costs is crucial, as both influence the financial health of the business. Explicit costs are direct payments like wages and raw materials, whereas implicit costs represent opportunity costs, such as the loss of potential income from alternative uses of the firm's resources.