# HWK5 - specific quantity of electricity? A specific...

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ECON 2010 HW #5 ln(Cost) = -8.55 + 0.82*ln(KWH) + 0.18*ln(Wage) + 0.60*ln(PFuel) + 0.22*ln(PCapital) What is the returns to scale implied by this cost function? A specific number is required, e.g. constant returns implies RTS = 1. Cost = 0.000194 + KWH^0.82 + Wage^0.18 + PFuel^0.60 + Pcapital^0.22 0.18=a/(a+b+c), 0.60=b/(a+b+c), 0.22=c/(a+b+c), 0.82=1/(a+b+c) Use the preceding equations to form a matrix. Solve. -0.82*a + 0.18*b + 0.18*c = 0 +0.60*a – 0.40*b + 0.60*c = 0 +0.22*a + 0.22*b – 0.78*c = 0 +0.82*a + 0.82*b + 0.82*c = 1 This results in a = 0.219512, b = 0.731707, and c = 0.268293. Because a+b+c = 1.22491 > 1, there are increasing returns to scale. (If a+b+c = 1, that represents constant returns to scale.) If fuel prices rise by 12 percent, what happens to the total cost of producing any
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Unformatted text preview: specific quantity of electricity? A specific percentage number is required. The elasticity of cost in relation to fuel prices is simply the coefficient of the logarithm of the latter. Multiplying 0.60, the elasticity, to 12%, the percentage increase in fuel prices, results in 7.2%, the percentage increase in cost. Extra Credit: If KWH of output increases by 10 percent, what does the cost function predict will be the resulting percentage change in the average cost per KWH? Recall k-1 = Elasticity of Average Cost where k = 1/(a+b+c) 1/(a+b+c)-1 = 0.82 1 = -0.183615-0.183615*10percent = -1.83615 // Cost will reduce by 1.83615%...
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