2 (30 marks) Bobby consumes two goods, food and gasoline His utility function is given by U( F , G ) 0 5ln( F ) ln( G ), where F represents the units of food consumed, and G represents the units of gasoline consumed Given this utility function, Bobbys marginal utility of food consumption is MU F 0 5 F , and his marginal utility of gasoline consumption is MU G 1 G (4 marks) Suppose the prices of food and gasoline are P F $1 unit and P G $4 unit in the base year Bobby will spend all his income I $120 on food and gasoline Write down Bobby's budget equation and diagram his budget line on a graph (Put the amount of food on the vertical axis and the amount of gasoline on the horizontal axis ) Whats the slope of Bobbys budget line Note that the slope of Bobbys indifference curve is his marginal rate of substitution (MRS) of gasoline for food, i e , the amount of food that he requires for giving up one unit of gasoline Mathematically, Bobbys MRS of gasoline for food is defined as the ratio MU G MU F (6 marks) Write down the two conditions for Bobbys utility maximizing basket ( G , F ), and calculate the values of F and G (2 marks) Label ( G , F ) on the graph with appropriate budget line and indifference curve (3 marks) Calculate the marginal utility per dollar of expenditure on food and the marginal utility per dollar of expenditure on gasoline at the utility maximizing basket ( G , F ) Are they the same Now, suppose the government imposes the following rationing of gasoline consumption G 10 (5 marks) Find Bobbys utility maximizing basket ( G R , F R ) with this government rationing policy Label ( G R , F R ) on the graph with appropriate budget line and indifference curve How much is Bobbys MRS of food for gasoline at the point ( G R , F R ) (2 marks) Is ( G R , F R ) a corner solution Why Lets assume that prices of food and gasoline change to P F $2 unit and P G $2 unit in the current year There is no rationing in the current year And Bobbys income in the current year is still $120 (3 marks) Find Bobbys utility maximizing basket ( F , G ) in the current year (5 marks) Calculate the Laspeyres index, Paasche index, and ideal cost of living index of obtaining the base year utility level for the price changes from the base year to the current year

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2. (30 marks) Bobby consumes two goods, food and gasoline. His utility function is given by U( F , G ) = 0.5ln( F )

2. (30 marks) Bobby consumes two goods, food and gasoline. His utility function is given by U(F, G) = 0.5ln(F) + ln(G), where F represents the units of food consumed, and G represents the units of gasoline consumed. Given this utility function, Bobbys marginal utility of food consumption is MU_F = 0.5/F, and his marginal utility of gasoline consumption is MU_G = 1/G.

(4 marks) Suppose the prices of food and gasoline are P_F = $1/unit and P_G = $4/unit in the base year. Bobby will spend all his income I = $120 on food and gasoline. Write down Bobby's budget equation and diagram his budget line on a graph. (Put the amount of food on the vertical axis and the amount of gasoline on the horizontal axis.) Whats the slope of Bobbys budget line?

Note that the slope of Bobbys indifference curve is his marginal rate of substitution (MRS) of gasoline for food, i.e., the amount of food that he requires for giving up one unit of gasoline. Mathematically, Bobbys MRS of gasoline for food is defined as the ratio MU_G/MU_F.

(6 marks) Write down the two conditions for Bobbys utility maximizing basket (G*, F*), and calculate the values of F* and G*.
(2 marks) Label (G*, F*) on the graph with appropriate budget line and indifference curve.
(3 marks) Calculate the marginal utility per dollar of expenditure on food and the marginal utility per dollar of expenditure on gasoline at the utility maximizing basket (G*, F*). Are they the same?

Now, suppose the government imposes the following rationing of gasoline consumption: G 10.

(5 marks) Find Bobbys utility maximizing basket (G^R, F^R) with this government rationing policy. Label (G^R, F^R) on the graph with appropriate budget line and indifference curve. How much is Bobbys MRS of food for gasoline at the point (G^R, F^R)?
(2 marks) Is (G^R, F^R) a corner solution? Why?

Lets assume that prices of food and gasoline change to P_F = $2/unit and P_G = $2/unit in the current year. There is no rationing in the current year. And Bobbys income in the current year is still $120.

(3 marks) Find Bobbys utility maximizing basket (F**, G**) in the current year.
(5 marks) Calculate the Laspeyres index, Paasche index, and ideal cost-of-living index of obtaining the base-year utility level for the price changes from the base year to the current year.