Define monopoly. How are price and output determined under it? [3+7] GROUP: B Short answer questions 4 × 5 = 20

Model Answer: Monopoly

Definition of Monopoly

A monopoly is a market structure characterized by the presence of a single seller of a product for which there are no close substitutes. The monopolist is the price maker (not price taker) and faces the entire industry demand curve as its Average Revenue (AR) curve. Key features include:

• Single seller: No competition; the monopolist dominates the market.
• No close substitutes: The product has unique characteristics with no perfect substitutes.
• High barriers to entry: Legal restrictions (patents, licenses), high capital requirements, or control over essential resources prevent new firms from entering.
• Price discrimination: The monopolist can charge different prices to different consumers if possible.
• Non-price competition: Uses advertising, branding, or product differentiation to maintain market power.

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Price and Output Determination in Monopoly

In a monopoly, price and output are determined where the Marginal Revenue (MR) equals Marginal Cost (MC), subject to the constraint that MC must cut MR from below. This is derived from profit maximization ($\text{Profit}=\text{Total Revenue (TR)}-\text{Total Cost (TC)}$).

Step-by-Step Explanation

1. Demand and Revenue Curves:

   • The monopolist’s AR (Average Revenue) curve is downward-sloping, identical to the market demand curve.
   • Marginal Revenue (MR) is always below AR (due to the law of demand: selling more units requires lowering price for all units). Formula: $$MR=AR+\left(\frac{d(AR)}{dQ}\right)Q$$ For a linear demand curve $P=a-bQ$, $MR=a-2bQ$.

2. Cost Curves:

   • The monopolist minimizes costs by producing where MC = MR (profit maximization condition).
   • MC curve must intersect MR from below (ensuring profit maximization).

3. Equilibrium Conditions:

   • First-order condition: $MR=MC$.
   • Second-order condition: MC must be rising at the point of intersection (to ensure a maximum, not minimum).
   • The price (P) is read from the AR curve at the profit-maximizing quantity ($Q^{\ast }$).

4. Graphical Illustration (Refer to the figure above):

   • The monopolist produces at $Q^{\ast }=4$ units (where $MR=MC$).
   • The price $P^{\ast }$ is determined by the AR curve at $Q^{\ast }$, i.e., $P^{\ast }=₹10$.
   • Profit per unit: $P^{\ast }-AC$ (Average Cost at $Q^{\ast }$).
   • Total Profit: $(P^{\ast }-AC)\times Q^{\ast }$.

5. Comparison with Perfect Competition:

   Feature	Monopoly	Perfect Competition
   Number of Firms	Single seller	Many small firms
   Price Control	Price maker (sets price)	Price taker (accepts market price)
   Output Level	Restricts output ($MR=MC$)	Produces where $P=MC=AR$
   Efficiency	Deadweight loss (underproduction)	Allocatively efficient ($P=MC$)
   Profit	Can earn supernormal profit	Zero economic profit in long run
   Non-price Competition	Advertising, branding	No advertising (price competition)

6. Mathematical Example: Suppose a monopolist faces the demand: $$P=20-2Q\text{and}MC=2+Q$$

   • Total Revenue (TR): $TR=P\times Q=(20-2Q)Q=20Q-2Q^2$.
   • Marginal Revenue (MR): $MR=\frac{d(TR)}{dQ}=20-4Q$.
   • Profit Maximization: Set $MR=MC$: $$20-4Q=2+Q⟹18=5Q⟹Q^{\ast }=3.6\text{ units}.$$
   • Price (P): Substitute $Q^{\ast }$ into demand: $$P^{\ast }=20-2(3.6)=₹12.8.$$
   • Profit: Calculate $TR-TC$ at $Q^{\ast }$.

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Key Takeaways

• Monopolies restrict output and charge higher prices compared to competitive markets, leading to deadweight loss.
• The profit-maximizing equilibrium occurs where $MR=MC$, with price read from the AR curve.
• Unlike perfect competition, monopolies can sustain economic profits in the long run due to barriers to entry.
• Government intervention (e.g., regulation, antitrust laws) may be required to curb monopolistic exploitation.