{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

econmodelingtestsoln

econmodelingtestsoln - Economics and modeling test Enter...

This preview shows pages 1–3. Sign up to view the full content.

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 [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 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. < ;

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 + 17.7778p2 + 15.1724p3 In[11]:= q2 @ p1_,p2_,p3_ D = q2form @ p1,p2,p3 D .solns @@ 1 DD Out[11]= 888. + 13.32p1 - 49.3333p2 + 16.5862p3 In[12]:= q3 @ p1_,p2_,p3_ D = q3form @ p1,p2,p3 D .solns @@ 1 DD Out[12]= 1050. + 11.2p1 + 9.07407p2 - 42.2414p3 In[13]:= q1 @ p1,p2,p3 D .initialpricerules Out[13]= 400.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 9

econmodelingtestsoln - Economics and modeling test Enter...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online