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Answered: - Need help on 2 and 4 please 2. A consumer has preferences


Need help on 2 and 4 please


2. A consumer has preferences represented by u(x1, x2) = min{x1, x2}, where xiis the quantity of good i = 1, 2. She faces prices (p1, p2) = (2, 1) and her income is $12.

(1) Draw on a graph some of this consumer?s indifference curves and her budget constraint. What is her optimal bundle?

(2) The price of good 2 rises to $3 and the consumer?s income stays the same. Usingblue ink, draw her new budget constraint on the graph. What is the new optimal bundle?

(3) What bundle would she choose if she faced the original prices and had justenough income to reach the new indifference curve? Draw with red ink the budget line that passes through this bundle at the original prices. How much income wouldthe consumer need at the original prices to have this (red) budget line?

(4) What is the maximum amount that she would pay to avoid the price increase?Is this the compensating or the equivalent variation?

(5) What bundle would the consumer choose if she faced the new prices and had just enough income to reach her original indifference curve? Draw with black ink the budget line that passes through this bundle at the new prices. How much income would she have with this budget?

(6) In order to be as well-off as she was with her original bundle, by how muchwould the consumer?s income have to rise? Is this the compensating or the equivalent variation?


Suppose there is a 40% chance that Bill, with a current wealth of $20,000.00, will contract a debilitating disease and suffer a loss of $10,000.00. Assume that the Bill has utility function U(x) = x1/2.

(1) Draw a graph with cd (consumption in the event of disease) on the horizontal axis and cnd (consumption in the event of no disease) on the vertical axis. If Bill purchases no insurance, plot Bill?s consumption on the graph, compute his expectedutility, and draw the indifference curve through his consumption.

(2) Compute the price of fair insurance (cost to consumer is equal to expected payout of insurance) in this scenario.

(3) Suppose Bill buys fair insurance covering half the cost of disease in the event of disease. Plot this bundle in the graph, compute the expected utility, and draw the indifference curve through it.

(4) Repeat the previous part but for full insurance.

(5) Compute Bill?s optimal insurance level, and the corresponding consumption ineach state and expected utility.

(6) Suppose the insurance company is running a discount and charges half of the fairprice. What is the new optimal insurance level and corresponding consumption andexpected utility? And if the insurance company charges 110% of the fair price?



Intermediate Microeconomics

 

Homework Set 6

 

Due on: March 25 (in Recitation)

 


 

Exercise 1

 

A consumer has quasilinear preferences and his Walrasian demand function for a good

 

is x? (p) = 15 ? p . This consumer is currently consuming 10 units of the good at a price

 

2

 

of $10 (a unit).

 

(1) How much money would he be willing to pay to have this amount rather than

 

no units at all? What is his level of (net) consumer surplus?

 

(2) The only supplier of the good decides to raise the price from $10 to $14. What

 

is the change in consumer?s surplus?

 

Exercise 2

 

A consumer has preferences represented by u(x1 , x2 ) = min{x1 , x2 }, where xi is the

 

quantity of good i = 1, 2. She faces prices (p1 , p2 ) = (2, 1) and her income is $12.

 

(1) Draw on a graph some of this consumer?s indi?erence curves and her budget

 

constraint. What is her optimal bundle?

 

(2) The price of good 2 rises to $3 and the consumer?s income stays the same. Using

 

blue ink, draw her new budget constraint on the graph. What is the new optimal

 

bundle?

 

(3) What bundle would she choose if she faced the original prices and had just

 

enough income to reach the new indi?erence curve? Draw with red ink the budget

 

line that passes through this bundle at the original prices. How much income would

 

the consumer need at the original prices to have this (red) budget line?

 

(4) What is the maximum amount that she would pay to avoid the price increase?

 

Is this the compensating or the equivalent variation?

 

(5) What bundle would the consumer choose if she faced the new prices and had

 

just enough income to reach her original indi?erence curve? Draw with black ink the

 

budget line that passes through this bundle at the new prices. How much income

 

would she have with this budget?

 

(6) In order to be as well-o? as she was with her original bundle, by how much

 

would the consumer?s income have to rise? Is this the compensating or the equivalent

 

variation?

 


 

1

 


 

Exercise 3

 

Consider a consumer who consumes two goods and has utility function

 

u(x1 , x2 ) = x2 +

 


 

?

 


 

x1 .

 


 

Income is m, the price of good 2 is 1, and the price of good 1 changes from p to

 

(1 + t)p. Compute the compensating variation, the equivalent variation, and the change

 

in consumer?s surplus for a change in the price of good 1, holding income and the price

 

of good 2 ?xed.

 

Exercise 4

 

Suppose there is a 40% chance that Bill, with a current wealth of $20,000.00, will

 

contract a debilitating disease and su?er a loss of $10,000.00. Assume that the Bill has

 

utility function U (x) = x1/2 .

 

(1) Draw a graph with cd (consumption in the event of disease) on the horizontal

 

axis and cnd (consumption in the event of no disease) on the vertical axis. If Bill

 

purchases no insurance, plot Bill?s consumption on the graph, compute his expected

 

utility, and draw the indi?erence curve through his consumption.

 

(2) Compute the price of fair insurance (cost to consumer is equal to expected payout

 

of insurance) in this scenario.

 

(3) Suppose Bill buys fair insurance covering half the cost of disease in the event of

 

disease. Plot this bundle in the graph, compute the expected utility, and draw the

 

indi?erence curve through it.

 

(4) Repeat the previous part but for full insurance.

 

(5) Compute Bill?s optimal insurance level, and the corresponding consumption in

 

each state and expected utility.

 

(6) Suppose the insurance company is running a discount and charges half of the fair

 

price. What is the new optimal insurance level and corresponding consumption and

 

expected utility? And if the insurance company charges 110% of the fair price?

 


 

2

 


 

 


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