MMEduopolysoln

MMEduopolysoln - 2011 - Steven Tschantz Duopoly Steven...

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© 2011 - Steven Tschantz Duopoly Steven Tschantz 2/8/11 Exercises Complete the following exercises. You can save a copy of this notebook, delete the material above, insert and evaluate your commands computing answers below, save your results, and email your final version to tschantz@math.vanderbilt.edu Clear all of the symbols we will be using. In[1]:= Clear @ p1, p2, q1, q2, a11, a12, a21, a22, b1, b2, mc1, mc2, profit1, profit2 D ; As above, suppose the demands for products are 1 and 2 are linear functions given by In[2]:= q1 @ p1_, p2_ D : = a11 * p1 + a12 * p2 + b1; q2 @ p1_, p2_ D : = a21 * p1 + a22 * p2 + b2; ± 1. At times x, y, and z, we observe the prices and demand for products 1 and 2, obtaining the following (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.; p2x = 40.; q1x = 100.; q2x = 120.; p1y = 55.; p2y = 40.; q1y = 80.; q2y = 130.; p1z = 50.; p2z = 45.; q1z = 105.; q2z = 100.; TableForm @88 p1x, p2x, q1x, q2x < , 8 p1y, p2y, q1y, q2y < , 8 p1z, p2z, q1z, q2z << , TableHeadings 88 "time x", "time y", "time z"
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MMEduopolysoln - 2011 - Steven Tschantz Duopoly Steven...

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