m256hw03soln

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Unformatted text preview: hypothetical) data. Determine the coefficients a11, a12, a21, a22, b1, and b2 of the linear demand functions that match this data. (Set up a system of equations, given as a list, and solve for the coefficients.) In[4]:= p1x 50.; p1y 55.; p1z 50.; TableForm "time p2x 40.; q1x 100.; q2x 120.; p2y 40.; q1y 80.; q2y 130.; p2z 45.; q1z 105.; q2z 100.; p1x, p2x, q1x, q2x , p1y, p2y, q1y, q2y , p1z, p2z, q1z, q2z , TableHeadings x", "time y", "time z" , "price 1", "price 2", "demand 1", "demand 2" Out[7]//TableForm= price 1 50. 55. 50. time x time y time z In[8]:= Out[8]= In[9]:= Out[9]= In[10]:= Out[10]= price 2 40. 40. 45. demand 1 100. 80. 105. demand 2 120. 130. 100. conditions q1 p1x, p2x q1x, q2 p1x, p2x q2x, q1 p1y, p2y q1y, q2 p1y, p2y q2y, q1 p1z, p2z 50. a11 55. a21 soln a11 40. a12 40. a22 b1 b2 100., 50. a21 130., 50. a11 40. a22 45. a12 b2 b1 q1z, q2 p1z, p2z 120., 55. a11 105., 50. a21 40. a12 45. a22 Solve conditions, a11, a12, a21, a22, b1, b2 4., a12 1., a21 2., a22 a11, a12, a21, a22, b1, b2 4., 1., 2., 4., 260., 180. 4., b1 260., b2 a11, a12, a21, a22, b1, b2 180. . soln 1 q2z b1 b2 80., 100. m256hw03soln.nb 11 2. Determine the own elasticities and cross elasticities for these products at time x. (The Mathematica function D[formula,variable] gives the partial derivative of the formula with respect to the variable.) In[11]:= Out[11]= In[12]:= Out[12]= elast11x D q1 p1, p2 , p1 p1 q1 p1, p2 . p1 p1x, p2 p2x D q1 p1, p2 , p2 p2 q1 p1, p2 . p1 p1x, p2 p2x D q2 p1, p2 , p1 p1 q2 p1, p2 . p1 p1x, p2 p2x D q2 p1, p2 , p2 p2 q2 p1, p2 . p1 p1x, p2 p2x 2. elast12x 0.4 In[13]:= elast21x Out[13]= 0.833333 In[14]:= elast22x Out[14]= 1.33333 3. Suppose constant marginal costs for the products are as given below and take fixed costs to be 0. Define functions profit1 and profit2 for the profits on products 1 and 2 (profit1[p1_,p2_]:=... and profit2[p1_,p2_]:=...). In[15]:= mc1 In[16]:= profit1 p1_, p2_ Out[16]= In[17]:= Out[17]=...
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This note was uploaded on 07/12/2013 for the course MATH 256 taught by Professor Schantz during the Spring '11 term at Vanderbilt.

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