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 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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