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Prof.
 Marek Weretka's
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Econ 301 Intermediate Microeconomics 
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Problem Set 4
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Problem 1 
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As in the previous problem set, Benjamin spends his time either watching
 movies 
\begin_inset Formula $(x_{1})$
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 (as you know he is taking advantage of "on demand" option, cable TV) or
 listening to the songs - MP3 downloaded from the Internet 
\begin_inset Formula $(x_{2})$
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.
 His preferences are 
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\begin_inset Formula $U(x_{1},x_{2})=4ln(x_{1})+ln(x_{2})$
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.
 
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His total income is 
\begin_inset Formula $m=100$
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, the price of MP3 is one dollar per each song (
\begin_inset Formula $p_{2}=1$
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).
 Suppose that the price of a movie drops from 
\begin_inset Formula $p_{1}=10$
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 to 
\begin_inset Formula $p_{1}=5$
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.
 
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a) By how much the "consumption" of movies changes due to the price drop?
 
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b) Are movies ordinary or Giffen goods? Explain why.
 
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c) By how much 
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 changes because movies are cheaper relative to MP3 (find substitution effect)
 
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d) How about the effect of increased purchasing power of Benjamin's income?
 (find income effect) 
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e) Is the income effect in d) positive or negative? Why? (Hint: is a movie
 a normal of inferior good?) 
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f) Show the total change, the substitution and income effects on the graph.
 
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Problem 2 
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Consider Trevor from our previous problem set.
 He begins the day with a strawberry milkshake (milk and strawberries mixed
 in proportion 1:5).
 His income is equal to m=200 , and one strawberry costs 
\begin_inset Formula $p_{2}=1$
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 .
 Suppose the price of milk drops from 
\begin_inset Formula $p_{1}=15$
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 to 
\begin_inset Formula $p_{1}=5$
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.
 
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a) What is the total change in demand for milk.
 
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b) What is a substitution effect 
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c) How about income effect 
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Problem 3 
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Miriam has quasilinear preferences over consumption of coffee 
\begin_inset Formula $(x_{1})$
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 and muffins 
\begin_inset Formula $(x_{2})$
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 given by 
\begin_inset Formula $U(x_{1},x_{2})=5ln(x_{1})+x_{2}$
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.
 Her income is equal to 
\begin_inset Formula $m=$
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$10, and 
\begin_inset Formula $p_{2}=$
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$1.
 
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a) Find MRS as a function of consumptions of two commodities.
 Write down two secrects of happiness.
 
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b) Find optimal consumption of 
\begin_inset Formula $x_{1}$
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 and 
\begin_inset Formula $x_{2}$
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 for arbitrary value of 
\begin_inset Formula $p_{1},p_{2},m$
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 using two secrets of happiness from a) (assume interior solution) 
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c) Suppose price of coffee drops from 
\begin_inset Formula $p_{1}=$
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$5 to 
\begin_inset Formula $p_{1}=$
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$1.
 Find substitution effect.
 
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d) Find income effect 
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Problem 4 
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Dave is initially endowed with 20 apples and 20 oranges 
\begin_inset Formula $ω=(20,20)$
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a) Assume 
\begin_inset Formula $p_{1}=p_{2}=2$
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.
 Write down Dave's budget constraint, and plot budget constraint in the
 graph.
 Mark all bundles on budget line for which Dave is selling apples and is
 buying oranges.
 
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b) Suppose 
\begin_inset Formula $U(x_{1},x_{2})=x_{1}x_{2}$
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.
 Find indifference curve that passes though endowment point analytically
 and find its slope (MRS) at the endowment point.
 Depict the curve and the slope in the graph.
 
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c) Assume 
\begin_inset Formula $p_{2}=2$
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 and find optimal choices of Dave under three scenarios: 
\begin_inset Formula $p_{1}=1,p_{1}=$
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2 and 
\begin_inset Formula $p_{1}=3$
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.
 Determine net demands of Dave for apples and oranges.
 
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d) Is Dave buying or selling apples on the market under the three scenarios?
 Explain why he is using such trading strategy by comparing MRS at the endowment
 point with relative price.
 
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e) Connect the three optimal bundles to obtain price offer curve and plot
 it on a graph with indifference curve passing though endowment point.
 Is your price offer curve located above the indifference curve? 
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Problem 5 
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Kate is not sure how many hours she should spend at work and we have to
 help her.
 Her total available time is 24h.
 She has no other source of income but salary.
 She is a lawyer, and a current wage rate for lawyers (per hour) is 
\begin_inset Formula $w=$
\end_inset

$100.
 She only consumes bananas that cost 
\begin_inset Formula $p_{c}=$
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$5 per pound.
 
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a) What is her real wage rate (wage rate in terms of bananas) ? 
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b) Show her budget set on the graph.
 
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Suppose her utility function is :
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\begin_inset Formula $U(C,R)=R×C$
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where R is leisure (or relaxation time) and C is consumption of bananas.
 
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c) Find her optimal time spent at work, the relaxation time and consumption
 of bananas.
 
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d) How your answer in c) would change if her wage rate was 
\begin_inset Formula $w=$
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$
\begin_inset Formula $200$
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.
 How would you explain the change (or possibly no change) in her labor supply?
 
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