Rumi has $100 and is deciding how to spend it on bread and wine. The price of bread is $2 and the price of wine is $2. (Both goods are infinitely divisible.)

Write down the budget constraint in terms ofax

1

+bx

2

=c

, wherex

1

is quantity of bread andx

2

is quantity of wine. (Since this is a linear equation, you could scalea

,b

, andc

by an arbitrary scalar. In this and subsequent questions, just letc

be the total budget in dollars.)

a=

unanswered

b=

unanswered

c=

unanswered

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Problem PS2.2.2

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Suppose the price of wine drops from $2 to $1 when a new source of grapes is found in Tashkent. Write down the new budget constraint.

a=

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b=

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c=

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Problem PS2.2.3

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Use the original prices ($2 for both bread and wine), but suppose that Rumi's income increases from $100 to $200 when he earns the patronage of the shah. Write down the new budget constraint.

a=

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b=

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c=

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Problem PS2.2.4

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Again return to the first budget constraint. Now suppose the government wants consumers to conserve bread, so it increases the price of bread to $4 for each additional loaf over 25 loaves. In other words, 26 loaves of bread will cost a consumer225+14=$54

.

Draw the budget constraint. What is the area under the new budget constraint?

(Note: We don't ascribe any intuitive meaning to this value. It is just a way to check that you have constructed the constraint correctly.)

unanswered