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Problem Set 2
Bogazici University
EC 101.05: Principles of Microeconomics
Due Thursday Oct 27, 2011
Note: Type everything but graphs and calculations for full credit. Completely label all
graphs for full credit. Homework assignments may not be submitted electronically. This
problem set (PS) is due on Thursday, October 27 at the beginning of class. If graded, the
maximum score is 100 points. Be sure to review the syllabus for details about problem sets and
their grading! Feel free to contact me via e-mail if you have specific questions about the PS.
Problem 1
Consider the perfectly competitive market for mechanical pencils.
a) Sketch a demand/supply diagram for the market for mechanical pencils. Label the
equilibrium price and quantity on your diagram.
b) You study survey data and observe that if mechanical pencils cost $4, then 4 wooden
pencils are demanded, while if mechanical pencils cost $10, 20 wooden pencils are
demanded. Calculate the Cross Price Elasticity of Demand for mechanical pencils and
wooden pencils. How are these two goods related?
c) Suppose the price of wooden pencils decreases. Draw the effects of this shift on your
diagram from part (a). Label the new equilibrium price and quantity. In a sentence or two,
explain why you changed your diagram in this manner. Explicitly state what happened to
equilibrium price and quantity.
Problem 2
Assume that a consumer’s Income Elasticity of Demand for Halk-ekmek bread is -0.2.
a) What does this value tell you about this good?
b) Sketch a demand/supply diagram for the market for Halk-ekmek bread. Label the
equilibrium price and quantity on your diagram. Suppose consumer’s income increases.
Draw the effects of this shift on your diagram from above. Label the new equilibrium
price and quantity. Explicitly state what happened to equilibrium price and quantity.
Problem 3
Consider the market for cigarettes. Suppose the market demand for cigarettes is given by
QD=40-4P and the market supply is QS=6P.
a) Find the equilibrium price and quantity and show this graphically.
b) Suppose the government decides that people should be buying fewer cigarettes, so
it imposes a sales tax of $1 per quantity. Assume consumers pay the tax. Calculate the
new equilibrium.
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c) Graphically show how this policy affects the prices and quantity.
d) Now consider an alternative policy where the tax is imposed on producers, i.e.
producers pay a tax of $1 per quantity. Calculate the new equilibrium.
e) Graphically show how this policy affects the prices and quantity.
f) For each policy, find the burden of the tax on both consumers and producers. Do
the results verify the conclusions we drew in class?
Problem 4:
Suppose the price of skateboards is $10 and the price of rollerblades is $5.
a) Draw the budget line for a consumer with an income of $100, putting skateboards
on the x-axis.
b) What is the slope of the budget constraint?
c) What happens when the price of rollerblades increases to $7? Graph it.
d) What happens when income drops to $50? Graph it.
Problem 5
The following table shows the utility of consumption of Pizza to Mario:
Quantity (Per month)
0
1
2
3
4
5
6
Total Utility (TL monetary value)
0
25
45
60
68
75
75
a) Calculate the marginal utility for each quantity consumed.
b) Suppose price of pizza is 15TL. How many pizzas should Mario consume this
month?
c) Derive and graph Mario’s demand for pizza.
Problem 6
Consider a mutant giant with one left hand and three right hands:
a- Give an example of a utility function that this giant might have in an environment
with 2 goods only: left hand gloves and right hand gloves. Justify your answer.
b- Draw hypothetical indifference curves corresponding to the utility function that
you specified in the previous part.
c- Draw a hypothetical budget line and argue where the optimal consumption bundle
of the giant should be.
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Problem 7
Consider an Mario whose utility over two goods X and Y is measured such that the
marginal utilities are as follows:
MUX=10-X
MUY=5-Y
Also, PX = 2, PY =1 and income, I=$10.
a) Write the equation of the budget line.
b) Write the condition for optimality of the consumption bundle.
c) Solve for the consumer’s optimal bundle of X and Y.
d) Graphically, drawing the budget constraint and our “general” indifference curves,
show the optimal consumption bundle.
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