Ap Micro 2023 Frq Set 1 Answers

AP Microeconomics 2023 FRQ Set 1 – Detailed Answer Guide

The 2023 AP Microeconomics Free‑Response Question (FRQ) Set 1 tests students’ ability to apply core microeconomic concepts to real‑world scenarios. Each question combines graphical analysis, algebraic manipulation, and concise written explanation. Below is a step‑by‑step walkthrough of the three FRQs, including the correct answers, the reasoning behind them, and the scoring rubrics that the College Board used. Use this guide to check your work, understand where points are earned, and refine your test‑taking strategy for future exams.

Overview of the Set

FRQ Set 1 consists of three multipart questions:

The total possible score is 30 points, which translates to roughly 30 % of the overall AP Micro exam score. Each sub‑part is awarded points for correct labeling, accurate calculations, and clear economic intuition.

Question 1 – Consumer Choice and Indifference Analysis

Prompt (paraphrased):
A consumer has a utility function (U(x,y)=x^{0.5}y^{0.5}). The prices are (P_x = $4) and (P_y = $2). Income is (I = $100).

(a) Derive the consumer’s demand functions for goods (x) and (y).
(b) Calculate the optimal bundle ((x^,y^)) given the income and prices above.
(c) Show how the optimal bundle changes if the price of good (x) falls to $2 while income and (P_y) remain unchanged.
(d) Explain, in words, why the consumer’s response to the price change is consistent with the law of demand.

Answer Key & Scoring| Part | What earns points | Typical points |

|------|-------------------|----------------| | (a) | Correctly setting up the Lagrangian (\mathcal{L}=x^{0.5}y^{0.5}+\lambda(I-P_xx-P_yy)) and solving the first‑order conditions to obtain (x^* = \frac{I}{2P_x}) and (y^* = \frac{I}{2P_y}). | 2 | | (b) | Substituting (I=100, P_x=4, P_y=2) → (x^* = \frac{100}{2·4}=12.5), (y^* = \frac{100}{2·2}=25). Correct labeling of the bundle on a graph (indifference curve tangent to budget line). | 2 | | (c) | New price (P_x'=2) → (x'^* = \frac{100}{2·2}=25), (y'^* = \frac{100}{2·2}=25). Show the shift of the budget line outward and the new tangency point. | 2 | | (d) | Explanation: When (P_x) falls, the consumer can afford more of good (x) while holding utility constant; the substitution effect leads to a higher quantity demanded of (x), and the income effect (positive for a normal good) reinforces this increase. Hence quantity demanded rises, illustrating the law of demand. | 2 | | Total | — | 8 (the remaining point is awarded for neat graphing and correct axis labels) |

Common pitfalls:

• Forgetting to divide income by 2 when deriving the demand functions (the Cobb‑Douglas utility yields equal expenditure shares).
• Mislabeling the axes (quantity of (x) on the horizontal axis, quantity of (y) on the vertical).
• Stating that the income effect is negative without checking whether the good is normal (it is, because both goods have positive income elasticity).

Question 2 – Firm Behavior in Perfect Competition Prompt (paraphrased): A perfectly competitive firm faces a market price (P = $15). Its total cost function is (TC(q)= 50 + 5q + q^{2}).

(a) Derive the firm’s marginal cost (MC) and average total cost (ATC) functions.
(b) Determine the profit‑maximizing output level (q^).
(c) Calculate the firm’s profit (or loss) at (q^).
(d) Sketch the firm’s short‑run supply curve and indicate the shutdown point.
(e) If the market price falls to $9, what is the new profit‑maximizing output and does the firm produce or shut down?

Answer Key & Scoring

Common pitfalls: - Confusing ATC with A