A1: PERFECT SUBSTITUTES..(a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 andY = 10? Create a table then graph/sketch the indifference curve through (10, 10).(b) What do we mean by a composite good? What does this composite good look like with thesepreferences? Show and explain.(c) State the consumer's utility maximization problem and express this in words. Sketch this in afigure and explain.(d) Show that demands are: X = 3M/[3Px + Py] and Y = M/[3Px + Py]. Hint: use the compositegood from (b).(e) Let prices be Px = $5, Py = $3 and income M = $1000. What is optimal X, Y, and utility? Showyour work.(f) Suppose Px rises to $6 and Py falls to $2 but income stays at $1000. Calculate the CompensatingVariation that ensures the consumer is no worse off nor better off with these price changes.Show and explain your work.A2: RISK and INSURANCE...Consider the following FIRE-INSURANCE PROBLEM where fire partially destroys a $500 house.EVENTFIRENO FIREPROBABILITY OUTCOME INSURANCE PAYOUT$100$5000.020.98$4000PREMIUM????(a) What do we mean when we say an agent is Risk Averse?(b) Assume utility is U(x) = V(x). Why does this utility function imply the agent is risk-averse? Use afigure/diagram to explain.(c) What is the expected payoff and expected utility of having no insurance for this agent?(d) What do we mean by certainty equivalent? What is the certainty equivalent of no insurance?(e) What is the maximum the agent will pay for complete insurance that pays out $400 in the caseof fire? Show your work.(f) Suppose insurance is incomplete and only pays out $300 in case of fire. What is the maximumthe agent will pay for insurance now? Show your work and explain relative to (e). Note: I aminterested in your solution technique more than the answer. So show your thought process.

“Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

A1: PERFECT SUBSTITUTES... (a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 and Y = 10? Create a table then graph/sketch the indifference curve through (10, 10). (b) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (c) State the consumer's utility maximization problem and express this in words. Sketch this in a figure and explain.

A1: PERFECT SUBSTITUTES... (a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 and Y = 10? Create a table then graph/sketch the indifference curve through (10, 10). (b) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (c) State the consumer's utility maximization problem and express this in words. Sketch this in a figure and explain.

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Chapter1: Making Economics Decisions

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Question

A1: PERFECT SUBSTITUTES..
(a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 and
Y = 10? Create a table then graph/sketch the indifference curve through (10, 10).
(b) What do we mean by a composite good? What does this composite good look like with these
preferences? Show and explain.
(c) State the consumer's utility maximization problem and express this in words. Sketch this in a
figure and explain.
(d) Show that demands are: X = 3M/[3Px + Py] and Y = M/[3Px + Py]. Hint: use the composite
good from (b).
(e) Let prices be Px = $5, Py = $3 and income M = $1000. What is optimal X, Y, and utility? Show
your work.
(f) Suppose Px rises to $6 and Py falls to $2 but income stays at $1000. Calculate the Compensating
Variation that ensures the consumer is no worse off nor better off with these price changes.
Show and explain your work.
A2: RISK and INSURANCE...
Consider the following FIRE-INSURANCE PROBLEM where fire partially destroys a $500 house.
EVENT
FIRE
NO FIRE
PROBABILITY OUTCOME INSURANCE PAYOUT
$100
$500
0.02
0.98
$400
0
PREMIUM
??
??
(a) What do we mean when we say an agent is Risk Averse?
(b) Assume utility is U(x) = V(x). Why does this utility function imply the agent is risk-averse? Use a
figure/diagram to explain.
(c) What is the expected payoff and expected utility of having no insurance for this agent?
(d) What do we mean by certainty equivalent? What is the certainty equivalent of no insurance?
(e) What is the maximum the agent will pay for complete insurance that pays out $400 in the case
of fire? Show your work.
(f) Suppose insurance is incomplete and only pays out $300 in case of fire. What is the maximum
the agent will pay for insurance now? Show your work and explain relative to (e). Note: I am
interested in your solution technique more than the answer. So show your thought process.

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(D)
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