based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium?
a. 20
b. 30
c. 40
d. there is not enough information given to determine the point of equilibrium.

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Market Equilibrium", "Supply Curve Analysis", "Demand Curve Analysis" ], "new_concepts": [], "current_concepts": [ "Market Equilibrium", "Supply Curve Analysis", "Demand Curve Analysis" ] } ## Determine the supply equation Using the *Supply Curve Analysis* knowledge point $$ \begin{aligned} &\text{Points on Supply (S): } (0, 20), (20, 30)\ &m_S = \frac{30 - 20}{20 - 0} = 0.5\ &P_S(Q) = 0.5Q + 20 \end{aligned} $$ ## Determine the demand equation Using the *Demand Curve Analysis* knowledge point $$ \begin{aligned} &\text{Points on Demand (D): } (0, 50), (20, 30)\ &m_D = \frac{30 - 50}{20 - 0} = -1\ &P_D(Q) = -Q + 50 \end{aligned} $$ ## Find the equilibrium point Using the *Market Equilibrium* knowledge point $$ \begin{aligned} &P_S(Q) = P_D(Q)\ &0.5Q + 20 = -Q + 50\ &1.5Q = 30 \implies Q = 20\ &P = -20 + 50 = 30 \end{aligned} $$

a. 20

b. 30

c. 40

d. There is not enough information given to determine the point of equilibrium.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Market Equilibrium" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the supply equation

Determine the demand equation

Find the equilibrium point

Answer: