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Problem Set 4 - Solutions

# Problem Set 4 - Solutions - function has constant returns...

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ECON – 301 Problem Set 4 – Solutions 1) In both instances, for low values of L the total product curve increases at an increasing rate. For K = 600, this happens for L < 200. For K = 1200, it happens for L < 400. - 5,000,000 10,000,000 15,000,000 20,000,000 25,000,000 30,000,000 35,000,000 0 200 400 600 800 Total Product Labor Total Product with K=600 - 50,000,000 100,000,000 150,000,000 200,000,000 250,000,000 300,000,000 0 500 1000 1500 Labor Total Product with K=1200

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ECON – 301 2) A general fixed proportions production function is of the form ) , min( bL aK Q . If we were to scale up all inputs by a factor (that is, replace K by K , and L by L ), the resulting output would be ) , min( ) , min( bL aK L b K a = Q . Therefore the production
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Unformatted text preview: function has constant returns to scale. 3) a) Since 9 K , we get 45 9 18 L which implies that L = 36/18 = 2. Therefore the firm’s total cost with this input combination is 4(2) + 5(9) = \$53. b) If the firm could operate optimally, it would choose labor and capital to satisfy the tangency condition: 5 4 1 2 2 L K , implying that . 4 8 10 L K Also, . 45 2 K KL Combining these two conditions, 18 K = 4.24 and L = 4.8. Now the firm’s expenditure would be 4(4.24) + 5(4.8) = \$41 approximately. Therefore the firm loses about \$12 because of its constraint on capital....
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Problem Set 4 - Solutions - function has constant returns...

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