based on the demand graph and the supply graph shown above, what is the price at the point of equilibrium?
a. 100
b. 70
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", "Demand Curve Analysis" ], "new_concepts": [ "Supply Curve Analysis" ], "current_concepts": [ "Market Equilibrium", "Demand Curve Analysis", "Supply Curve Analysis" ] } ## Find the demand equation Using the *Demand Curve Analysis* knowledge point $$ \begin{aligned} &\text{Points on demand curve: } (20, 70), (40, 40), (60, 10)\ &m_D = \frac{40 - 70}{40 - 20} = -1.5\ &P - 70 = -1.5(Q - 20) \implies P = -1.5Q + 100 \end{aligned} $$ ## Find the supply equation Using the *Market Equilibrium* knowledge point $$ \begin{aligned} &\text{Points on supply curve: } (20, 70), (40, 80), (60, 90)\ &m_S = \frac{80 - 70}{40 - 20} = 0.5\ &P - 70 = 0.5(Q - 20) \implies P = 0.5Q + 60 \end{aligned} $$ ## Solve for equilibrium Using the *Market Equilibrium* knowledge point $$ \begin{aligned} &-1.5Q + 100 = 0.5Q + 60\ &40 = 2Q \implies Q = 20\ &P = 0.5(20) + 60 = 70 \end{aligned} $$

a. 100

b. 70

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

Explanation:

Find the demand equation

Find the supply equation

Solve for equilibrium

Answer: