Wyandotte Chemical Company sells various chemicals to the automobile industry. W

Question

Wyandotte Chemical Company sells various chemicals to the automobile industry. Wyandotte currently sells 30,000 gallons of polyol per year at an average price of $15 per gallon. Fixed costs of manufacturing polyol are $90,000 per year and total variable costs equal $180,000. The operations research department has estimated that a 15 percent increase in output would not affect fixed costs but would reduce average variable costs by 60 cents per gallon. The marketing department has estimated the arc elasticity of demand for polyol to be

Explanation / Answer

Suppose p is the price % change in Quantity = 15 % % change in price = x 15/x = - 2 x= -15/2 = -7.5 % prices should be reduce by 7.5 % so change is (p-15)/avg price avg price = (15+p)/2 so 2(p-15)/(15+p) = - 0.075 so prices per gallon = $13.9156 so reduction of = 15 -13.9156= $1.08 a) Change in Total Revenue = 13.9156 x 1.15 x 30000 - 15 x 30000 = $ 30088.2 (increase ed by $30088) average cost = 180000/30000 = $6 b) Total cost = Final - Intial = [90000+0.4 x6x1.15x30000]-[90000+180000] = -97200 (reduced by $97200) c) profits increased by = 97200+30088 = $127288 intial = TR - TC =$ 180000 after increase in quantity profit = $307288

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