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October 21st, 2012, 07:39 PM   #1
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Managerial Econ help...

Hey everyone, I am working on this question and I cannot seem to solve the last part:

Question: Ivy is a typical student and she spends her $200 allowance on booze(X) and books(Y). Her utility function is given by: and Px=$5 and Py:$5

(a) Solve for Ivy's optimal purchases of X and Y
(b) The government believes that the sum of the intelligence on the planet is a constant and the population keeps growing. A tax is imposed on books and the price doubles, i.e Py=$10. How many books will Ivy purchase now?
(c) Using your answers from (a) and (b) above, calculate Ivy's price elasticity of demand for books and her cross price elasticity of demand for booze with respect to the price of books.
(d) Sketch the demand curve
(e) If the government had asked how much of her income, at most she would be willing to give up (lump sum of income tax) to prevent the increase in the price of books, what would her answer be, assuming of course, she does not lie?


My Answer:
(a) I used the Langrangian method and got X=10 y=20
(b) Again, used lagrangian however changed the price of Y to 10, and got X=10 and Y=20
(c) Price elasticity of demand for books = 1
Cross price elasticity of demand = 0...but why?
(d) no need
(e) I dont know how to solve this!!! I have been working on this for a while!! someone please help
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October 22nd, 2012, 07:00 AM   #2
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Re: Managerial Econ help...

Quote:
Originally Posted by pomazebog
(a) I used the Langrangian method and got X=10 y=20
Should be X = 20, Y = 20. Typo?

Quote:
Originally Posted by pomazebog
(b) Again, used lagrangian however changed the price of Y to 10, and got X=10 and Y=20
Right.

Quote:
Originally Posted by pomazebog
(c) Price elasticity of demand for books = 1
Cross price elasticity of demand = 0...but why?
(d) no need
(e) I dont know how to solve this!!! I have been working on this for a while!! someone please help
I think these will get easier now that you know the right answer to (a).
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October 22nd, 2012, 03:33 PM   #3
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Re: Managerial Econ help...

Sorry, in the question I originally typed out, Px=10, and Py=5.

I am mainly looking for help for part (E). I literally do not know how to do it. I make a budget constraint, but I make the y-axis books and the x-axis income. But I dont know how to calculate the amount of income she is willing to give up
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October 22nd, 2012, 06:26 PM   #4
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Re: Managerial Econ help...

Figured it out....I forgot the final two steps to multiply by the quantity then subtract from original income.
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