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Total Cost Function

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Superior Metals Company has seen its sales volume decline over the last few years as the result of rising foreign imports. In order to increase sales (and hopefully, profits), the firm is considering a price reduction on luranium - a metal that it produces and sells. The firm currently sells 60,000 pounds of luranium a year at an average price of $10 per pound. Fixed costs of producing luranium are $250,000. Current variable costs per pound are $5. The firm has determined that the variable cost per pound could be reduced by $.50 if production volume could be increased by 10 percent (fixed costs would remain constant). The firm's marketing department has estimated the arc elasticity of demand for luranium to be -1.5. How much would Superior Metals have to reduce the price of luranium in order to achieve a 10 percent increase in the quantity sold? After the price cut, what would total revenue, total costs, total profits be and identify the total cost function?

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Solution Preview

Qo = 60,000
Po = 10
FC = 250,000
AVC = 5

After the cost reduction,
AVC = 5 - 0.50 = 4.50
Q1 = 60,000*(1+10%) = ...

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