3. a) Maximise utility u = x0.6 y0.5 subject to the budget constraint 5x+6y=120. Use the Hessian%3Dto test the second-order conditionb) A monopolistic producer of two related goods faces the demand functionsx=50–2 P,+ Pyy=55+4p,-8p,His total cost function is TC = 0.2x² +2xy+0.4 y² . Find the profit maximising level ofoutput if a production quota requires 2x+ 6 y= 300. Use the Bordered Hessian to test thesecond-order condition

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a) Maximise utility u = x0.6 y0.5 subject to the budget constraint 5x+6%3D120. Use the Hessian to test the second-order condition

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

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

3. a) Maximise utility u = x0.6 y0.5 subject to the budget constraint 5x+6y=120. Use the Hessian
%3D
to test the second-order condition
b) A monopolistic producer of two related goods faces the demand functions
x=50–2 P,+ Py
y=55+4p,-8p,
His total cost function is TC = 0.2x² +2xy+0.4 y² . Find the profit maximising level of
output if a production quota requires 2x+ 6 y= 300. Use the Bordered Hessian to test the
second-order condition

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