1 4 Consumer choice with an endowment (questions)

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Microeconomics II 
Undergraduate degree in Economics 
 
 
Review Exercises – 1.4. Consumer choice with initial endowment 
 
Exercise 9.2. from Bergstrom and Varian’s book (2006) “Workouts in Intermediate 
Microeconomics”, pp. 111-112 
Mario has a small garden where he raises eggplant and tomatoes. He consumes some of 
these vegetables, and he sells some in the market. Eggplants and tomatoes are perfect 
complements for Mario, since the only recipes he knows use them together in a 1:1 
ratio. One week his garden yielded 30 kg of eggplant and 10 kg of tomatoes. At that 
time the price of each vegetable was €5/kg. 
 
a) What is the monetary value of Mario’s endowment of vegetables? 
b) Sketch (in a graph) Mario’s budget constraint. Which consumption bundle will 
he choose? Sketch (in a graph) the indifference curve that goes through Mario’s 
chosen consumption bundle. 
c) Suppose that before Mario makes any trades, the price of tomatoes rises to 
€15/kg, while the price of eggplant stays at €5/kg. What is the monetary value of 
Mario’s endowment now? Sketch (in a graph) his new budget constraint. Which 
consumption bundle will he choose now? 
 
d) Suppose that (at the original prices) Mario had sold his entire crop at the market 
for a total of $200, intending to buy back some tomatoes and eggplant for his 
own consumption. Before he had a chance to buy anything back, the price of 
tomatoes rose to $15/kg, while the price of eggplant stayed at $5/kg. Sketch (in a 
graph) his new budget constraint. Which consumption bundle will Mario 
choose? 
 
e) Assuming that the price of tomatoes rose to $15/kg from $5/kg before Mario 
made any transactions, by how much has the demand for tomatoes changed due 
to the Slutsky substitution effect? How much has the demand for tomatoes 
changed due to the ordinary and endowment income effects? How much was the 
total change in the demand for tomatoes? 
 
 
Exercise 9.7. from Bergstrom and Varian’s book (2006) “Workouts in Intermediate 
Microeconomics”, pp. 116-117 
 
Mr. Cog works in a machine factory. He can work as many hours per day as he wishes 
at a wage rate of w. Let C be the number of dollars he spends on consumer goods and let 
R be the number of hours of leisure that he chooses. 
 
a) Assume that Mr. Cog earns $8 an hour and has 18 hours per day to devote to 
labor or leisure, and he has $16 of nonlabor income per day. Write an 
equation for his budget constraint between consumption and leisure. Sketch 
(in a graph) the previous budget constraint and his endowment. If Mr. Cog 
Microeconomics II 
Undergraduate degree in Economics 
 
 
has the utility function ( ) CRCRU =, , how many hours of leisure per day 
will he choose? How many hours per day will he work? 
 
b) Suppose that Mr. Cog’s wage rate rises to $12 an hour. Sketch (in a graph) 
his new budget constraint. If he continued to work exactly as many hours as 
he did before the wage increase, how much more money would he have each 
day to spend on consumption? However, how many hours will he choose to 
work, and how much more is going to increase his consumption with this 
new budget constraint? 
 
c) Suppose that Mr. Cog still receives $8 an hour but that his nonlabor income 
rises to $48 per day. Sketch (in a graph) his new budget constraint. How 
many hours does he choose to work? 
 
d) Suppose that Mr. Cog has a wage of $w per hour, a nonlabor income of $m, 
and that he has 18 hours a day to divide between labor and leisure. Cog’s 
budget constraint has the equation wmwRC 18+=+ . Find the amount of 
leisure that Cog will demand as a function of wages and of nonlabor income. 
(Hint: Notice that this is the same as finding the demand for R when the 
price of R is w, the price of C is 1, and income is m + 18w.) Determine, as 
well, Mr. Cog’s supply function for labor.