Jamilah's choice of bread and fish. Jamilah's preferences over the consumption of bread and fish are represented by the utility function u(x,y)=(xy) 1/2
, where x and y denote the quantities of bread and fish, respectively, measured in hectograms. Jamilah's budget is $100 and the prices per hectogram are p x
=$5 and p y
=$2. (a) Write down Jamilah's optimization problem. (10 points) (b) Graph the budget line and outline the set of feasible consumption bundles. (5 points) (c) Compute Jamilah's marginal rate of substitution of fish for bread. (5 points) (d) What is the general expression for Jamilah's indifference curve? (5 points) (e) What is the general expression for the slope of Jamilah's indifference curve? How does it relate to her marginal rate of substitution? (5 points) (f) Compute Jamilah's optimal consumption bundle. What are her expenditure shares? What is Jamilah's utility level associated with her choice of bread and fish? (5 points) (g) Let {9,y 1
},{5,y 2
} and {1,y 3
} be three bundles of bread and fish that make Jamilah indifferent to her own choice. Compute y 1
,y 2
and y 3
. Compute the total purchase price of the three bundles. Are the bundles feasible? (5 points) (h) Can you compute the exact values of y 1
,y 2
and y 3
simply using the ratio of prices p y
p x
? Can you approximate the values of y 1
,y 2
and y 3
simply using the ratio of prices p y
p x
? Please motivate your answer. (5 points) (i) Now assume that Jamilah's preferences are instead represented by u(x,y)= (xy) 2
. Show that Jamilah's choice does not change. Why doesn't it? (5 points) Jamilah's choice of bread and fish. Jamilah's preferences over the consumption of bread and fish are represented by the utility function u(x,f 1
)=(xy) 1/2
, where x and y denote the quantities of bread and fish, respectively, measured in hectograms. Jamilah's budget is $100 and the prices per hectogram are p x
=$5 and p y
=$2. (a) Write down Jamilah's optimization problem. (10 points) (b) Graph the budget line and outline the set of feasible consumption bundles. (5 points) (c) Compute Jamilah's marginal rate of substitution of fish for bread. (5 points) (d) What is the general expression for Jamilah's indifference curve? (5 points) (e) What is the general expression for the slope of Jamilah's indifference curve? How does it relate to her marginal rate of substitution? (5 points) (f) Compute Jamilah's optimal consumption bundle. What are her expenditure shares? What is Jamilah's utility level associated with her choice of bread and fish? (5 points) (g) Let {9,y 1
},{5,y 2
} and {1,y 3
} be three bundles of bread and fish that make Jamilah indifferent to her own choice. Compute y 1
,y 2
and y 3
. Compute the total purchase price of the three bundles. Are the bundles feasible? (5 points) (h) Can you compute the exact values of y 1
,y 2
and y 3
simply using the ratio of prices p y
p 2
? Can you approximate the values of y 1
,y 2
and y 3
simply using the ratio of prices p y
p z
? Please motivate your answer. (5 points) (i) Now assume that Jamilah's preferences are instead represented by u(x,y)= (xy) 2
. Show that Jamilah's choice does not change. Why doesn't it?
