Unformatted text preview: Economics and modeling test
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4/7/11 Questions
This is an open book, open computer test. Complete the following questions. You are to work individually in class for
approximately 75 minutes. Honor code provisions apply. Email your final version to [email protected]
1. Define linear demand functions for three products q1[p1,p2,p3], q2[p1,p2,p3], and q3[p1,p2,p3] such
that for prices p1=25., p2=27., and p3=29. the demands are q1=400., q2=370., and q3=350., and the
matrix of own and crossprice elasticities of demand is given as follows (so elast[[i,j]] is the elasticity
of the quantity of product i with respect to the price of product j).
Clear elast ; elast 4.
0.9
0.8 1.2
3.6
0.7 1.1
1.3 ;
3.5 2. Let c be a parameter in the range 5 to 5. Suppose the demands for two products are given by the
following formulas. Suppose the marginal costs for the two products are respectively mc1=40. and
mc2=35. As a function of c, compute the competitive Nash equilibrium prices for separate firms
owning the products and then compute the profit maximizing prices for a single, merged firm owning
both products. Illustrate (numerically or with a plot) and explain why both prices are higher for the
merged case than the competitive case if c>0, but both prices are lower for the merged case than the
competitive case if c<0.
Clear c, p1, p2, q1, q2 ;
q1 p1_, p2_
1000. 50. c q2 p1_, p2_
1200. 50. c 1000.
12. p1
1200.
c p1 50. c 12. c c p1 c p2 15. p2 c p2
50. p1 15. p2 3. A hotair balloonist plans to offer tethered balloon rides at a fair. Rides will last for t minutes, in the
range 2 to 20 minutes, for a price of p dollars, in the range $5 to $30. The balloonist estimates an
average of 20+3t2p people per hour will want to ride, at least that is for t and p where this formula
gives a positive value, but having a single balloon that can carry only a single passenger the balloonist
is actually limited to at most 60/t rides in an hour. The marginal cost for a ride may be taken to be
zero, since the balloon must be kept heated to near neutral buoyancy between rides anyway. Find the t
and p that give the balloonist the greatest revenue. 2 econmodelingtest.nb 3. A hotair balloonist plans to offer tethered balloon rides at a fair. Rides will last for t minutes, in the
range 2 to 20 minutes, for a price of p dollars, in the range $5 to $30. The balloonist estimates an
average of 20+3t2p people per hour will want to ride, at least that is for t and p where this formula
gives a positive value, but having a single balloon that can carry only a single passenger the balloonist
is actually limited to at most 60/t rides in an hour. The marginal cost for a ride may be taken to be
zero, since the balloon must be kept heated to near neutral buoyancy between rides anyway. Find the t
and p that give the balloonist the greatest revenue. ...
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 Spring '11
 Schantz
 Math

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