Naomi's expenditure function defined for a month for two commodities, Cassava (Q₁) and Banana (Q₂) is given by: [125P, PU 8 Where P₁ is the price of Cassava (P₁>0), P2 is the price of banana (P2>0) and U is the fixed utility. The income of Naomi is m, where m > 0. Derive the indirect utility function for Naomi (Hint: Use the duality conditions) Using the Shephard's Lemma condition, derive Naomi's Hicksian demand function for Cassava (Q₁¹). Using the Roy's identity, derive Naomi's Marshallian demand function for Banana (Q₂). Using the answer in (i), evaluate Naomi's maximum utility level when the price per i. ii. 111. iv. E =

Naomi's expenditure function defined for a month for two commodities, Cassava (Q₁) and Banana (Q₂) is given by: [125P, PU 8 Where P₁ is the price of Cassava (P₁>0), P2 is the price of banana (P2>0) and U is the fixed utility. The income of Naomi is m, where m > 0. Derive the indirect utility function for Naomi (Hint: Use the duality conditions) Using the Shephard's Lemma condition, derive Naomi's Hicksian demand function for Cassava (Q₁¹). Using the Roy's identity, derive Naomi's Marshallian demand function for Banana (Q₂). Using the answer in (i), evaluate Naomi's maximum utility level when the price per i. ii. 111. iv. E =

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

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Rhea is determining how many gallons of milk (M) and loaves of bread (B) to purchase. Use the information in italics to answer the bolded question below: Rhea's marginal utility function for milk: MUN • Rhea's marginal utility function for bread: M = 0.5M-2 MUB = 0.5MB-1/2 • Rhea has $60 to spend on bread and milk. • The price of milk (Pm) is $3/gallon of milk. • The price of bread (Pb) is $1/loaf of bread. • For the sake of computation, assume that bread is the horizontal axis good (i.e., good X) and milk is the vertical axis good (i.e., good Y). When you set up the optimal budget decision rule for Rhea's consumer problem, which of the following statements best describes how much she will buy of both goods at her consumer equilibrium? O For each gallon of milk, Rhea will buy 1/3 loaf of bread. O For each gallon of milk, Rhea will buy 3 loaves of bread. For each gallon of milk, Rhea will buy 1 loaf of bread. O For each gallon of milk, Rhea will buy 6 loaves of bread.
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