2. Consider an individual who not only consumes goods x and y, but also needs a mini-mum amount of x = xo to survive. Her (Stone-Geary) utility function is given byU(x, y) = (x — xo)¹/²y¹/²Let prices be pa, Py and income is I > Pro.(a) Show that this individual maximizes utility by spending (I-Pro) + Pro ongood rand(I - Pro) on good y. Provide an economic interpretation for thisresult. [Hint: It might help to define z = x - xo and I = I - Pro. Then find theoptimal z (and therefore x = z + xo) and y]

The consumer maximises his utility at the point where the slope of the budget constraints is equal…

(a) Show that this individual maximizes utility by spending (1 - Pro) + Pªo on good rand(I - Pro) on good y. Provide an economic interpretation for this result. [Hint: It might help to define z = x-xo and I = I - P₂o. Then find the optimal z (and therefore x = z + xo) and y]

(a) Show that this individual maximizes utility by spending (1 - Pro) + Pªo on good rand(I - Pro) on good y. Provide an economic interpretation for this result. [Hint: It might help to define z = x-xo and I = I - P₂o. Then find the optimal z (and therefore x = z + xo) and y]

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Form Utility

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.

Question

2. Consider an individual who not only consumes goods x and y, but also needs a mini-
mum amount of x = xo to survive. Her (Stone-Geary) utility function is given by
U(x, y) = (x — xo)¹/²y¹/²
Let prices be pa, Py and income is I > Pro.
(a) Show that this individual maximizes utility by spending (I-Pro) + Pro on
good rand(I - Pro) on good y. Provide an economic interpretation for this
result. [Hint: It might help to define z = x - xo and I = I - Pro. Then find the
optimal z (and therefore x = z + xo) and y]

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