Quiz 14 Cost Minimization Ans

Quiz 14 Cost Minimization Ans - y = 3? The expenditure of...

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Shomu Banerjee ECON 201 COST MINIMIZATION ANSWERS Suppose a firm has a production function: y = [min{ x 1 , 3 x 2 }] 1/2 where y is the output and x 1 and x 2 are inputs. (a) What is the returns-to-scale for this production function? y o = [min{ x 1 , 3 x 2 }] 1/2 y n = [min{ tx 1 , 3 tx 2 }] 1/2 = [ t min{ x 1 , 3 x 2 }] 1/2 = t 1/2 [min{ x 1 , 3 x 2 }] 1/2 = t 1/2 y o DRS (b) In the graph below, an isoquant for y = 3 is shown. The prices of the inputs are w 1 = $1 and w 2 = $2. Draw the isocost line corresponding to an expenditure of $12. See the solid red line. 10 15 5 10 5 x
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(c) What is the cost-minimizing expenditure for
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Unformatted text preview: y = 3? The expenditure of $12 is insufficient to produce the output level of 3 but sliding the isocost up as shown by the dashed red line shows that an expenditure of $15 will produce this output level in the cheapest way. (d) Calculate the cost function c ( w 1 , w 2 , y ). From the production function, square both sides. Then it follows that x 1 * = y 2 and x 2 * = y 2 /2. Therefore the cost function is c ( w 1 , w 2 , y ) = w 1 y 2 + w 2 y 2 /3 = ( w 1 + w 2 /3) y 2 ....
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Quiz 14 Cost Minimization Ans - y = 3? The expenditure of...

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