Firm's Production Decision: Revenues and Profits

Revenue

• Total Revenue (TR) = Price (P) * Quantity (Q): $TR = P \times Q$
• Average Revenue (AR) = Total Revenue / Quantity: $AR = \frac{TR}{Q} = P$ (equals the demand curve)
• Marginal Revenue (MR) = Change in Total Revenue / Change in Quantity: $MR = \frac{\Delta TR}{\Delta Q}$ (extra revenue from selling one more unit)
• When the demand curve is downward sloping, MR < Price.

Marginal and Total Revenue

• If Demand is a straight line, MR(0) = P(0), and the MR curve is twice as steep as the Demand curve.

Demand, Marginal Revenue, and Total Revenue

• When MR is positive but falling, total revenue is increasing at a slower rate.
• When MR is zero, total revenue is unchanged (unit elastic).
• When MR is negative, total revenue is falling (price inelastic).

Costs, Revenues, and Profits

• Profit = Total Revenue - Total Cost
• Abnormal/Supernormal Profits: Revenue > Total Costs (P > AC)
• Normal Profits: Revenue = Total Costs ($P = AC$) (break-even point)
• Losses: Revenue < Total Costs (P < AC)

Profit Maximization

• Occurs when Marginal Revenue = Marginal Cost ($MR = MC$).
• This condition must hold in both the short-run (SMC) and the long-run (LMC).

Maximizing Profits

• Short-Run: Profits are maximized when $MR = SMC$ at $Q^*$ (optimal quantity), provided the firm stays in business.
• Long-Run: Profit-maximizing output is where $MR = LMC$. Check for losses at $Q^*$. If no losses, the firm stays in business.

Production Decisions

• Short-Run: Produce if price $P(Q)$ >= Average Variable Cost $SAVC(Q)$. Shut down if P(Q) < SAVC(Q).
• Long-Run: Produce if price $P(Q)$ >= Long-Run Average Cost $LAC(Q)$. Shut down if P(Q) < LAC(Q).

Measuring Profits at Optimal Quantity

• Total Profit = (Price - Average Total Cost) * Optimal Quantity: $(P – ATC) \times Q^*$

Business Objectives

• Classical Assumption: Firms maximize profits.
• Separation of ownership and control in large firms.
• Managers may pursue different objectives (e.g., size, growth).
• Profit is a source of internal finance and a benchmark of success.