3. (10 points) calculate the income elasticities for the following demand functions.

(a) (5 points) $x(p, m) = \frac{m}{2p}$
(b) (5 points) $x(p, m) = \frac{10}{p}$

Question

3. (10 points) calculate the income elasticities for the following demand functions.

(a) (5 points) $x(p, m) = \frac{m}{2p}$
(b) (5 points) $x(p, m) = \frac{10}{p}$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Income Elasticity of Demand", "Partial Derivatives" ], "current_concepts": [ "Income Elasticity of Demand", "Partial Derivatives", "Demand Functions" ] } ## Define the income elasticity formula $$ \epsilon_m = \frac{\partial x(p, m)}{\partial m} \cdot \frac{m}{x(p, m)} $$ ## Calculate elasticity for function (a) $$ \begin{aligned} x(p, m) &= \frac{m}{2p} \ \frac{\partial x}{\partial m} &= \frac{1}{2p} \ \epsilon_m &= \frac{1}{2p} \cdot \frac{m}{\frac{m}{2p}} = 1 \end{aligned} $$ ## Calculate elasticity for function (b) $$ \begin{aligned} x(p, m) &= \frac{10}{p} \ \frac{\partial x}{\partial m} &= 0 \ \epsilon_m &= 0 \cdot \frac{m}{\frac{10}{p}} = 0 \end{aligned} $$ ## Question (a) The income elasticity is $1$. ## Question (b) The income elasticity is $0$. { "subject": "Business", "question_type": "Multi-part", "knowledge_point": [ "Business", "Economics", "Income Elasticity of Demand" ] }

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QUESTION IMAGE

Question

Explanation:

Define the income elasticity formula

Calculate elasticity for function (a)

Calculate elasticity for function (b)

Answer:

Question (a)

Question (b)