Compilation - CHIANG act

Compilation - CHIANG act - 11.6 Number 1 Given the change...

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Unformatted text preview: 11.6 Number 1 Given the change in the production function in the former example, we solve for optimal values of q1 & q2 Setting up our revenue, cost, and profit functions : In[98]:= Clear @ c D In[99]:= r = p10 * q1 + p20 * q2 c = 2 * q1 + 2 * q2 ^ 2 = r- c Out[99]= p10 q1 + p20 q2 Out[100]= 2 q1 + 2 q2 2 Out[101]=- 2 q1 + p10 q1 + p20 q2- 2 q2 2 Solving for the new optimla levels of q1 & q2, we get : For q1 : In[103]:= D @ , q1 D Out[103]=- 2 + p10 For q2 : D @ , q2 D p20- 4 q2 Solving for the new profit : In[104]:= * = p10 * H- 2 + p10 L + p20 * H p20- 4 q2 L- 2 * H- 2 + p10 L + 2 * H p20- 4 q2 L ^ 2 Out[104]=- 2 H- 2 + p10 L + H- 2 + p10 L p10 + p20 H p20- 4 q2 L + 2 H p20- 4 q2 L 2 The new profit is negative, therefore, its economic meaning is that the firm will incur losses if they adopt the new cost function. Number 2 Clear @ q1, q2, r, c, , p1, p2 D Given the 2 direct demand functions, we solve for the inverse demand equations. By solving we get : Solve @ q1 40- 2 * p1- p2, p1 D :: p1 fi 1 2 H 40- p2- q1 L>> Solve @ q2 35- p1- p2, p2 D 88 p2 fi 35- p1- q2 << We set up the firm ' s revenue function, given by : r = 1 2 H 40- p2- q1 L * q1 + H 35- p1- q2 L * q2 1 2 H 40- p2- q1 L q1 + H 35- p1- q2 L q2 We also define the cost function, given by : c = q1 ^ 2 + 2 * q2 ^ 2 + 10 10 + q1 2 + 2 q2 2 Solving for profit maximization , we define profit as TR- TC, defines as r- c in solution : = r- c- 10 + 1 2 H 40- p2- q1 L q1- q1 2 + H 35- p1- q2 L q2- 2 q2 2 Solving for optimal valeus when profit = H FOC L we derive the profit function wrt to each variable. We get : Solve @8 D @ , q1 D 0, D @ , q2 D < , 8 q1, q2 <D :: q1 fi 40- p2 6 , q2 fi 35- p1 6 >> We now have the optimal values for goods 1 & 2 To check whether the values satisfy the sufficient conditions for a maximum,...
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This note was uploaded on 09/22/2011 for the course ECON 101 taught by Professor Mr.tull during the Spring '11 term at De La Salle University.

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Compilation - CHIANG act - 11.6 Number 1 Given the change...

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