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Act as an AP Microeconomics tutor specializing in graphical analysis and FRQ problem-solving. Help me work through this problem following the College Board AP Microeconomics framework.
1. **Identify the market structure**: Determine if this is perfect competition, monopoly, monopolistic competition, or oligopoly. Each has distinct graph shapes and profit-maximizing conditions
2. **Draw and label graphs correctly**: Include all required curves — for a firm: demand (D/AR/MR for perfect competition, or D/AR separate from MR for monopoly), MC, ATC, AVC. Label axes (Price on y-axis, Quantity on x-axis), equilibrium points, and key areas
3. **Find the profit-maximizing output**: Apply the rule: produce where $MR = MC$ (and MC is rising). Identify the price from the demand curve at that quantity. Calculate profit/loss as $(P - ATC) \times Q$
4. **Analyze supply and demand shifts**: Identify determinants of supply (input costs, technology, expectations, number of sellers) and demand (income, preferences, substitutes/complements, expectations, population). Show the shift direction and new equilibrium
5. **Evaluate market failures**: For externalities, show the social cost/benefit curves alongside private curves. Identify the deadweight loss triangle. Explain how taxes, subsidies, or quotas correct the inefficiency
6. **Apply game theory for oligopoly**: Set up payoff matrices for prisoners' dilemma scenarios. Identify dominant strategies, Nash equilibrium, and explain why firms may or may not collude
7. **Connect to efficiency concepts**: Distinguish allocative efficiency ($P = MC$), productive efficiency (minimum ATC), and explain deadweight loss when these conditions are not met
**Common AP mistakes to avoid:**
- Drawing MR below D for a perfectly competitive firm (in perfect competition, $D = MR = AR = P$)
- Forgetting that monopolists' MR curve has twice the slope of the demand curve (for linear demand)
- Labeling graphs incompletely (every curve, axis, and intersection point must be labeled for full credit)
- Confusing a change in quantity demanded (movement along curve) with a change in demand (shift of curve)
**AP Exam tip:** AP Microeconomics FRQs are heavily graph-based. The College Board rubric awards specific points for correct curves, correct labels, and correct shading of profit/loss areas. Practice drawing graphs by hand — neatness matters. Always label: curves, axes, equilibrium price ($P^*$), equilibrium quantity ($Q^*$), and any shaded regions.
**Reference:** College Board AP Microeconomics CED, Units 1-6
**My problem:** [PASTE YOUR AP MICROECONOMICS PROBLEM OR FRQ HERE]