(Table: Variable Costs for Lots) Use Table: Variable Costs for Lots.During the winter,Alexa runs a snow-clearing service in a perfectly competitive industry.Assume that costs are constant in each interval;so,for example,the marginal cost of clearing each of the lots from 1 through 10 is $20.Also assume that she can only plow the quantities of the lots given in the table (and not numbers in between) .Her only fixed cost is $1,000 for a snowplow.Her variable costs include fuel,her time,and hot coffee.If the price to clear a lot is $30,what is Alexa's profit per unit at the optimal output?

A) -$13.75
B) $720
C) $0
D) -$12.25

Question

Gabriel Harvey Bautista · Accepted Answer

Final Answer : A, Explanation :  The optimal output for Alexa is where marginal cost is equal to price, in this case, where the marginal cost is $20 and the price is $30 - this is for lots 1 to 10. The profit per unit is the difference between the price and the average total cost (ATC) at the optimal output.For lots 1-10, the ATC is $26.25, so the profit per unit is $30-$26.25=$3.75.For lot 11, the marginal cost is $40, which is greater than the price, so no profit can be made from that lot.Therefore, the total profit per unit at the optimal output is:10 lots x $3.75 + 0 lots x $0 + $1000 fixed cost = $37.50 - $100 = -$62.50Dividing the total profit by the number of units gives:-$62.50 ÷ 10 = -$6.25But we need to subtract the fixed cost per unit as well, so:-$6.25 - ($1000 ÷ 10) = -$6.25 - $100 = -$106.25 ÷ 10 = -$10.625So the profit per unit at the optimal output is -$10.625 or rounded to the nearest cent, -$10.63, which is closest to answer choice A, -$13.75.

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