econmodelingtestsoln

econmodelingtestsoln - Economics and modeling test Enter...

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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). In[1]:= Clear @ elast D ; In[2]:= elast =- 4. 1.2 1.1 0.9- 3.6 1.3 0.8 0.7- 3.5 ; Solution In[3]:= Clear @ p1, p2, p3, q1, q2, q3, q1form, q2form, q3form, a11, a12, a13, a21, a22, a23, a31, a32, a33, b1, b2, b3, initialpricerules, eqns, solns D ; In[4]:= q1form @ p1_, p2_, p3_ D = a11 * p1 + a12 * p2 + a13 * p3 + b1; q2form @ p1_, p2_, p3_ D = a21 * p1 + a22 * p2 + a23 * p3 + b2; q3form @ p1_, p2_, p3_ D = a31 * p1 + a32 * p2 + a33 * p3 + b3; In[7]:= initialpricerules = 8 p1 fi 25., p2 fi 27., p3 fi 29. < ; In[8]:= eqns = 8 q1form @ p1, p2, p3 D 400., q2form @ p1, p2, p3 D 370., q3form @ p1, p2, p3 D 350., D @ q1form @ p1, p2, p3 D , p1 D * p1 q1form @ p1, p2, p3 D elast @@ 1, 1 DD , D @ q1form @ p1, p2, p3 D , p2 D * p2 q1form @ p1, p2, p3 D elast @@ 1, 2 DD , D @ q1form @ p1, p2, p3 D , p3 D * p3 q1form @ p1, p2, p3 D elast @@ 1, 3 DD , D @ q2form @ p1, p2, p3 D , p1 D * p1 q2form @ p1, p2, p3 D elast @@ 2, 1 DD , D @ q2form @ p1, p2, p3 D , p2 D * p2 q2form @ p1, p2, p3 D elast @@ 2, 2 DD , D @ q2form @ p1, p2, p3 D , p3 D * p3 q2form @ p1, p2, p3 D elast @@ 2, 3 DD , D @ q3form @ p1, p2, p3 D , p1 D * p1 q3form @ p1, p2, p3 D elast @@ 3, 1 DD , D @ q3form @ p1, p2, p3 D , p2 D * p2 q3form @ p1, p2, p3 D elast @@ 3, 2 DD , D @ q3form @ p1, p2, p3 D , p3 D * p3 q3form @ p1, p2, p3 D elast @@ 3, 3 DD< . initialpricerules Out[8]= : 25. a11 + 27. a12 + 29. a13 + b1 400., 25. a21 + 27. a22 + 29. a23 + b2 370., 25. a31 + 27. a32 + 29. a33 + b3 350., 25. a11 25. a11 + 27. a12 + 29. a13 + b1- 4., 27. a12 25. a11 + 27. a12 + 29. a13 + b1 1.2, 29. a13 25. a11 + 27. a12 + 29. a13 + b1 1.1, 25. a21 25. a21 + 27. a22 + 29. a23 + b2 0.9, 27. a22 25. a21 + 27. a22 + 29. a23 + b2- 3.6, 29. a23 25. a21 + 27. a22 + 29. a23 + b2 1.3, 25. a31 25. a31 + 27. a32 + 29. a33 + b3 0.8, 27. a32 25. a31 + 27. a32 + 29. a33 + b3 0.7, 29. a33 25. a31 + 27. a32 + 29. a33 + b3- 3.5 > In[9]:= solns = Solve @ eqns, 8 a11, a12, a13, a21, a22, a23, a31, a32, a33, b1, b2, b3 <D Out[9]= 88 a11 fi - 64., a12 fi 17.7778, a13 fi 15.1724, a21 fi 13.32, a22 fi - 49.3333, a23 fi 16.5862, a31 fi 11.2, a32 fi 9.07407, a33 fi - 42.2414, b1 fi 1080., b2 fi 888., b3 fi 1050. << In[10]:= q1 @ p1_, p2_, p3_ D = q1form @ p1, p2, p3 D . solns @@ 1 DD Out[10]= 1080.- 64. p1 + 17.7778 p2 + 15.1724 p3 In[11]:= q2 @ p1_, p2_, p3_ D =...
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This document was uploaded on 10/28/2011 for the course MATH 256 at Vanderbilt.

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econmodelingtestsoln - Economics and modeling test Enter...

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