Ecns 300: Midterm 3
Due: Friday, October 19, 2012 (at beginning of class)
1. If two goods are perfect complements, will the income and substitution effects differ when one uses Hicks
decomposition rather than Slutsky decomposition? What about if the two goods are perfect substitutes? Explain
and demonstrate your answers using (large) well-labeled graphs that you refer to in your explanations.
For each of the following games, indicate (a) if there is a dominate solution— if there is one, state what it is and
explain how you got it, and (b) all Nash equilibriums.
Player 1
I
Up
Center
Down
Left
1,1
2,4
3,3
Player 2
Middle
3,4
2,5
0,4
II
Right
2,1
8,1
0,9
Player 1
2.
Up
Center
Down
Left
1,1
0,5
0,0
Player 2
Middle
5,0
4,4
0,0
Right
0,0
0,0
3,3
3. Draw the “normal form” (i.e., the grid form similar to those shown above in problem 2) for the following game and
identify both the pure- and mixed-strategy equilibria. In the mixed-strategy Nash equilibrium, determine each
firm’s expected profit level if it enters the market.
There are two firms that are considering entering a new market, and must make their decision without knowing
what the other firm has done. Unfortunately the market is only large enough to support one of the two firms. If
both firms enter the market, then they will each make a loss of $10 million. If only one firm enters the market,
that firm will earn a profit of $50 million. If a firm does not enter that market, it will have no effect one way or the
other on their bottom line.
Extra Credit:
4.
Along a stretch of beach 'down the shore' there are 500 children in five clusters of 100 each. They are clustered in this
fashion due to the location of the lifeguard stands. The stands are labeled A, B, C, D, E. Each child buys one ice cream
cone per day.
There are two rival ice cream vendors named Ben and Jerry. Each morning they roll their wagons down to the beach for
business at 10 AM. They must locate their wagon at the exact location of one of the clusters. The children always go to the
nearest vendor. If there is a vendor in a cluster then all 100 children buy from that vendor. For clusters without a vendor, 50
of the children will walk to an adjacent cluster with a vendor for ice cream, only 20 will walk as far as two clusters, none will
walk three or more clusters for ice cream. If both Ben and Jerry are located in the same cluster then they each get 50% of
the demand for ice cream at that location. If Ben and Jerry locate in different clusters then children that are equidistant from
both of them will be equally split.
Ben
Jerry
A
B
C
A
85, 85
100, 170
125, 195
B
170, 100
110, 110
150, 170
C
195, 125
170, 150
E
195, 125
D
E
D
125, 195
110, 110
170, 100
100, 170
85, 85
a.
Fill in the missing cells in the payoff matrix. To get you started: If Ben chooses B and Jerry chooses C, then Ben will
sell 150 cones (100 from his own cluster and 50 walking over from A) and Jerry will sell 170 cones (100 from his own
cluster plus 50 walkers from D and 20 walkers from E).
b.
Suppose that Jerry plays B. What is Ben's best response?
c.
How many dominant solutions are there in this game? What are they? (If there are, explain how you derived the
solution(s).)
d.
How many Nash equilibria are there? List any.
e.
Are there Pareto Optimal outcomes in this game? List any.
f.
Does this example help explain why Home Depot located across the street from Lowes. Explain why or why not*.
(Note: Lowes, originally doing business as Eagle, was at the West End location for several years before Home Depot
located across the street. Use that fact.)
* If this example does NOT explain the close location, what additional assumptions or considerations might you add to the
second paragraph above to change the payoffs so that the outcome of the game would explain the observed phenomenon?
Note: Lowes and Home Depot are pretty close to each other in Bozeman and too many other cities to be mere coincidence.