Key Problem Set _3

# Key Problem Set _3 - Key Problem Set #3 8.14 To find the...

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Key Problem Set #3 8.14 To find the short run cost function when Hannah and Sam are initially remodeling 200 square feet per week, we first need to figure out how much capital they are using when they do this. This is the amount of capital that they will be stuck with in the short run. The problem starts as usual: R W L K = β α 000 , 1 \$ 000 , 1 \$ 5 . 0 5 . 0 = L K 1 = L K K = L The second condition to be satisfied is the production function: Q = 10 L 0.5 K 0.5 Q = 10 L 0.5 ( L ) 0.5 Q = 10 L L = Q /10 With Q = 200, L = 20. Therefore, K is also 20. This is their fixed amount of capital in the short run, which is a fixed cost of \$1,000(20), or \$20,000. When their capital is fixed at 20 units, the production function becomes 20 10 L Q = , which, when solved for L yields: L = Q 2 /2000. Multiplying this equation for L by the wage rate of \$1,000 gives the variable cost function VC ( Q ) = Q 2 /2. The short run total cost function is the sum of the fixed and variable cost: 2 000 , 20 ) ( 2 200 Q Q C SR + = To figure out the long-run cost function, we return to the result for L above, where Q was not fixed, L = Q /10. Since K = L , this means that K is also equal to Q /10. Therefore, the long-run cost function is: C LR ( Q ) = RK + WL C LR ( Q ) = 1,000( Q /10) + 1,000( Q /10) C LR ( Q ) = 200 Q

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8.15 To find the short run cost function when Hannah and Sam are initially remodeling 200 square feet per week, we first need to figure out how much capital they are using when they do this. This is the amount of capital that they will be stuck with in the short run. The problem starts as usual: R W L K = β α 000 , 1 \$ 000 , 1 \$ 25 . 0 25 . 0 = L K 1 = L K K = L The second condition to be satisfied is the production function: Q = 10 L 0.25 K 0.25 Q = 10 L 0.25 ( L ) 0.25 Q = 10 L 0.5 L 0.5 = Q /10 L = Q 2 /100 With
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## This note was uploaded on 06/09/2008 for the course BUAD 351 taught by Professor Eastin during the Spring '07 term at USC.

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Key Problem Set _3 - Key Problem Set #3 8.14 To find the...

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