econmodelingtest

econmodelingtest - Economics and modeling test Enter your...

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Unformatted text preview: Economics and modeling test Enter your name here 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 tschantz@math.vanderbilt.edu 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 cross-price 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 hot-air 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+3t-2p 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 hot-air 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+3t-2p 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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