Suppose that an individual has $400 in total income to spend, and they gain utility from two

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Question:

Suppose that an individual has $400 in total income to spend, and they gain utility from two
goods: (i) School (S), and (ii) Food (F). Suppose that the price of Schooling is $40 per unit and
the price of Food is $10 per unit.

Draw the budget line for this individual with Schooling on the x-axis and Food on the y-
axis. Label the x-intercept and y-intercept for this budget constraint. Call this Budget
Constraint 1.

Now suppose that the government decides to subsidize the price of schooling, providing a
household with a $20 per unit subsidy for each unit of Schooling consumed up until the 5th unit
of Schooling. However, they pay for this by increasing the price of Schooling by $20 for every
unit purchased after the 5th unit of Schooling. Draw this new budget line for this individual with Schooling on the x-axis and Food on
the y-axis. Label the x-intercept, y-intercept, and any kinks for this budget constraint.
Call this Budget Constraint 2.3. What is the slope of Budget Constraint 2 for each section of this budget constraint?
Show your work.

Suppose now that the previous subsidy for schooling is removed, and the government instead
institutes a “Free Lunch Program”. For each unit of Schooling that an individual purchases, they
receive a free unit of Food (for $0).

Draw this new budget line for this individual with Schooling on the x-axis and Food on
the y-axis. Label the x-intercept, y-intercept, and any kinks for this budget constraint.
Call this Budget Constraint 3.

What is the slope of Budget Constraint 3 for each section of this budget constraint?
Show your work.

NOTE: For the rest of this problem set, I would suggest using a Figure with Budget Constraint 1,
Budget Constraint 2, and Budget Constraint 3 all of the same figure.

Suppose that when faced with Budget Constraint 1, this individual chooses to consume 6 units
of Schooling and 16 units of Food ({ S , F } = { 6 , 16 }).

Suppose also that when faced with Budget Constraint 2, this individual chooses to consume 8
units of Schooling and 12 units of Food ({ S , F } = { 8 , 12 }).

Suppose also that when faced with Budget Constraint 3, this individual chooses to consume 5
units of Schooling and 25 units of Food ({ S , F } = { 5 , 25 }).

Do these choices satisfy the Weak Axiom of Revealed Preferences (WARP)? Why or why
not? You will need to thoroughly explain your answers to receive credit for this
question.

Do these choices satisfy the Strong Axiom of Revealed Preferences (SARP)? Why or why
not? How do you know?