Daniel and Kjell are writing a paper together. Daniel is the PhD supervisor and thus is the first to decide how many hours, hp. to put into the project. After observing the amount of time that Daniel contributes, Kjell decides how many hours, hK. to contribute. Daniel's utility function is 12(hp+ hx)5 -hp Kjell's utility function is 14(hp+hx)0.-hx How many hours does Kjell spend on the project? Select one alternative: 00 O 49 O 26 O 32

Daniel and Kjell are writing a paper together. Daniel is the PhD supervisor and thus is the first to decide how many hours, hp. to put into the project. After observing the amount of time that Daniel contributes, Kjell decides how many hours, hK. to contribute. Daniel's utility function is 12(hp+ hx)5 -hp Kjell's utility function is 14(hp+hx)0.-hx How many hours does Kjell spend on the project? Select one alternative: 00 O 49 O 26 O 32

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.2P

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Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).
An estate agent advertises its houses in two media; Daily Graphic and Ghanaian Times. The agent believes that there is a relationship between the sales S and the amounts spent on the two advertising media. The relationship is given by; where, d is the amount spent in Daily Graphic and g is the amount spent in Ghanaian Times. The estate’s agent fee is 12½% and this includes the cost of adverting. If the agent has planned to spend only 200 thousand Ghana Cedis on advertisement, show how it should be allocated between the two media in order to maximize net profit.
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i. Write down the Lagrangian form and solve the utility maximization problem. ii. Assume that the income increases from 100 to $101. What is the increase in the optimal value of u(x,y)?