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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Answered: a) Maximise utility u = x0.6 y0.5…

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

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Let Utility be given by U(x,y)=x^2 y^2 With a budget contraint p_x x+p_y y=Y Let px = 10 Let py = 2 Y = 100 Walk through the optimization process and identify the optimal choice for this consumer in both x and y (Hint: the MUx = 2xy2 and MUy = 2x2y) How much utility is this consumer receiving by consuming the optimal level of x and y? Use your answer in part b,the information from this problem, and excel to draw the budget constraint and the indifference curve at the optimal choice of x and y.
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Find the attached fie.
A young consumer has to decide how to spend his spare time. He can either watch movies x or play online video games y. Each round of the game cost 20 and each movie cost 20. He has 200 dollars to spend each week. In addition, he has time constraint. He can spend no more than 20 hours for entertainment each week. A movie last 2 hours and playing a game takes about 1 hour. His utility is given by √xy. Use the Kuhn-Tucker condition to find his optimal choice. (Assume that x and y can take any value, not necessarily integers.) Does the solution satisfy the necessary and sufficient condition for a maximum?
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