1. Worksheet 1
1- Sharon has the following utility function: U(X,Y) = X + Y where X is her consumption of
candy bars, with price PX = $1, and Y is her consumption of espressos, with PY = $3.
a. Derive Sharon’s demand for candy bars and espressos.
b. Assume that her income I = $100. How many candy bars and how many espressos
will Sharon consume?
c. What is the marginal utility of income?
2- Maurice has the following utility function: U(X,Y) = 20X + 80Y − X2 − 2Y2,where X is
his consumption of CDs, with a price of $1, and Y is his consumption of movie videos,
with a rental price of $2. He plans to spend $41 on both forms of entertainment.
Determine the number of CDs and video rentals that will maximize Maurice’s utility.
a- Then, you are given 3 tradable permits. Your neighbor, whose plant is much older than
yours, offers to pay you $250 for each permit you are willing to sell him. You should
_________.
3- Ernie’s utility function is U(x, y) = 32xy. He has 1 units of good x and 10 units of good y.
Waldo’s utility function for the same two goods is U(x, y) = x + 2y. Waldo has 5 units of
x and 5 units of y. The MRS for Ernie at his current bundle is _____ and the MRS for
Waldo is_____ .
4- Malcom eats roast beef and smokes Camels. Roast beef is $4 per pound and Camels are
$3 per pack. He currently chooses to consume 5 pounds of beef and 5 packs of cigarettes
per week.
a- Draw Malcom’s budget set. What is Malcom’s weekly income?
b- If Malcom wanted to smoke more cigarettes at what rate would have to give up beef?
Suppose that Malcom’s income increases to $45 and the price of cigarettes
simultaneously increases to $5 per pack. Draw his new budget set. Not knowing
anything about Malcom’s preferences except what was revealed by his oringinal
choice, is it possible to say whether Malcom is better off or worse off with the new
budget set? Explain.

2. 5- William has $250 to spend on food and a composite good. The price of food is $1 per
unit. The price of the composite good is $1 per unit.
a- Draw William’s budget set.
b- Suppose that the rule prohibiting non-food purchases is difficult to enforce and William
can sell his food stamp for $0.50 on the dollar. Draw his budget set.
6- Consider trying to sell your junky old car on the used car market. Some people love old
cars, see restoration potential in them and therefore have high reservation prices. Others
see them as quick fixes when their other car breaks suddenly. The latter group just needs
a car quickly and is not willing to pay much for a car. Hence, they have low reservation
prices. The following list of numbers is a list of the reservation prices of the 7 people who
are currently looking to buy a used car similar to yours: 1000, 900, 800, 750, 740, 300,
150.
a- Draw the demand curve for your used car (note: you can’t sell a fraction of a car).
b- Say you value your used car at 100 for sentimental reasons. If you are able to auction
off your car in (1) and ascending price (English) auction or (2) a descending price
(Dutch) auction, what price would you get? Draw another graph with the market
supply curve to support your prediction.
c- Now say you have 3 old cars (same model and year but different condition). You
value the first at $50, the second at $100 and the third at $150. If you auction them off
using the English auction (and the demand is the same as above) how much revenue
would you expect to get?
7- Eddie has $10 to spend on meatball sandwiches, good X, and root beer sodas, good Y.
a- If the price of a meatball sandwich is $5 and the price of root beer is $2, formulate and plot
Eddie’s budget constraint.
b- Assume the price of root beer decreases to $1. Formulate and plot his new budget
constraint.
c- Suppose Eddie’s income doubles to $20 and the prices of the good are the same as in (a).
What is the new budget constraint? Plot it.
8- Explain whether the following statements are true or false.

3. a- The marginal rate of substitution diminishes as an individual moves downward along
the demand curve.
b- The level of utility increases as an individual moves downward along the demand
curve.
9- What are a Pareto efficient and Pareto inefficient?
10- Extreme Cases of Indifference Curves
11- Given any two cars, I always prefer the one that is bigger and faster. Given this
information, are my preferences transitives? Are they complete?
12- An agent consumes quantity (x1; x2) of goods 1 and 2. She has utility u(x1; x2) = x1=2 1
x1=22
(a) Derive the MRS.
(b) Show that preferences are convex.