Ralph consumes apples (A) and bananas (B). His Marshallian demand for bananas is 10.5 p0.2 6p7 B* = (a) Find and interpret the income elasticity of demand for bananas (еÂ,1) and interpret the value. Are bananas an inferior or normal good? (b) Find the own price elasticity of demand for bananas (еB,PB) and interpret the value. Does the own price elasticity of demand for bananas depend on the value of PB? (c) Find the cross price elasticity of demand for bananas (eBPA) and interpret the value. Are bananas and apples gross substitutes or gross complements?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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**Demand Analysis: Ralph's Consumption of Apples and Bananas**

Ralph consumes apples (A) and bananas (B). His Marshallian demand for bananas is given by the equation:

\[ B^* = \frac{I^{0.5} p_A^{0.2}}{6p_B^{0.7}} \]

**Questions for Analysis:**

(a) **Income Elasticity of Demand for Bananas (\(e_{B,I}\))**: 

- Find and interpret this elasticity to determine if bananas are an inferior or normal good.

(b) **Own Price Elasticity of Demand for Bananas (\(e_{B,p_B}\))**:

- Calculate and interpret this elasticity to understand how sensitive the demand for bananas is to changes in their own price. Also, assess whether this elasticity depends on the value of \(p_B\).

(c) **Cross Price Elasticity of Demand for Bananas (\(e_{B,p_A}\))**:

- Determine and interpret this elasticity to conclude whether bananas and apples are gross substitutes or gross complements.
Transcribed Image Text:**Demand Analysis: Ralph's Consumption of Apples and Bananas** Ralph consumes apples (A) and bananas (B). His Marshallian demand for bananas is given by the equation: \[ B^* = \frac{I^{0.5} p_A^{0.2}}{6p_B^{0.7}} \] **Questions for Analysis:** (a) **Income Elasticity of Demand for Bananas (\(e_{B,I}\))**: - Find and interpret this elasticity to determine if bananas are an inferior or normal good. (b) **Own Price Elasticity of Demand for Bananas (\(e_{B,p_B}\))**: - Calculate and interpret this elasticity to understand how sensitive the demand for bananas is to changes in their own price. Also, assess whether this elasticity depends on the value of \(p_B\). (c) **Cross Price Elasticity of Demand for Bananas (\(e_{B,p_A}\))**: - Determine and interpret this elasticity to conclude whether bananas and apples are gross substitutes or gross complements.
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