Problem Set 6

Problem Set 6 - up to have the same level of utility as if...

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UCLA Economics 11 – Fall 2010 Professor Mazzocco Problem Set 6 Due by November 12 before 9:00am in the box located outside room 2221E, Bunche Hall Question 1) Ms Ramirez has the following utility function: U(x,y)= ln(x)+ln(y) Her total income is equal to I and she faces prices Px for good x and Py for good y. a) Calculate the Marshallian demands and Hicksian demands. b) Find the expenditure function. c) Suppose Px=10, Py=1 and I=22. If Px increases by 1%, what is the percentage change in the Marshallian demand functions for the goods x and y? What is the percentage change in the Hicksian demand functions for the goods x and y? (Hint: compute the elasticities) d) Are x and y gross substitutes? Are they net substitutes? e) How much additional income is necessary in order to compensate Ms Ramirez for the price change? (Hint: use the compensating variation) f) Suppose that the price didn’t change. What is amount of income that Ms Ramirez has to give
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Unformatted text preview: up to have the same level of utility as if the price had changed? Question 2) Mr Macleod likes to drink wine. He has the option to consume two different products, 1 liter of red wine (X) or 1.6 liters of white wine (Y). X and Y are perfect substitutes. Each liter of wine gives Mr Macleod 1 unit of utility. a) Write Mr Macleod utility function. b) Suppose that Px=5. Calculate the Marshallian demand for Y. Draw a graph for this demand (Y as function of Py). c) Now suppose that initially Px=5 and Py=10. But then the price of y changes to $7. Calculate the total change in demand for y. Explain your result. Question 3) The preferences of an individual are represented by the following utility function: U(x,y)= ln(x)+ 2y a) Determine if x and y are gross substitutes or gross complements. b) Determine if x and y are net substitutes or net complements....
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Problem Set 6 - up to have the same level of utility as if...

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