Solution to Exercise 8

Solution to Exercise 8 - Solution to Exercise 8.8.and...

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Solution to Exercise 8.8…and beyond. Given: Q = 10 L .2 K .3 ; w = $1500; r = $1000. Find the least-cost combination of L and K to produce Q = 100. Find the cost of producing 100. Find short-run total cost function assuming that K is fixed at the level you found above. Find the long-run total cost function. Least-cost means a tangency between isocost and isoquant: MRTS LK = W/R For Cobb-Douglas production function, MRTS LK = α K/ β L. In this case, α = 0.2, and β = 0.3. Therefore, .2K/>3L=1500/1000, or K = 9/4 L . Note that this is the equation for the expansion path for this Cobb-Douglas function and the given wage and rental rates. Plug K = 9/4 L back into the production function: 100 = 10 L .2 (9/4) .3 L .3 to find the optimal level of L for 100 units of Q to be L* = 61.4739. Now plug back into the expansion path relation to find optimal K* = 138.3162. This is the least-cost combination to produce Q = 100 units. To find the cost associated with this combination, use the cost equation: C = WL+RK: C = (1500)(61.4739) + (1000)(138.3162) = $230,527
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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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