Question

Cory has opened a ride-sharing business, and it has become fairly complex as she now owns half of the vehicles herself while her drivers own the rest. Cory's costs can be represented by the function c(y)=y3−2.00y2+30.00y+23.00, where y represents the number of rides. 1st attempt Part 1 (1 point)See Hint At what positive number of rides provided will Cory's average variable cost (AVC) be equal to her marginal cost (MC)? (Give your answer to two decimals.) Part 2 (1 point)See Hint What is the lowest price per ride at which Cory would ever operate? $ (Give your answer to two decimals.) Part 3 (1 point)See Hint Suppose that the price per ride drops to the exact price you found in Part 2 and that Cory remains in business in the short run. Remember that total profits are revenue minus costs. They can be divided by output to determine profits per ride. What is Cory's profit per ride at that price? $ (Give your answer to two decimals.)

Answer 1

c(y)=y3−2.00y2+30.00y+23.00

Part 1.

For MC: differentiate c with respect to y

MC= dc/dy= 3y2-4.00y+30.00

For AVC= c/y

AVC= y2-2.00y+30.00 (23.00 it not included because it ia fixed cost as it arise at y=0)

MC=AVC

3y2-4.00y+30.00=y2-2.00y+30.00

2y2-2.00y=0

2y(y-1.00)=0

y= 0 or 1.00

Part 2. A lowest point at which firm can operate is point where it can cover atleast its variable cost.

Lowest point at which Carry would operate is at lowest point of AVC which is the point where MC intersect with it. MC intersect AVC at y=1.00, So AVC=  (1.00)2-2.00(1.00)+30.00= $29.00. It is also the lowest price.

Part 3. If p=$29.00, so y=1.00

Profit= Total revenue - total cost= p*y-(y3−2.00y2+30.00y+23.00)= $29.00(1.00)-(1.00-2.00+30.00+23.00)

=29.00-52= - $23 (loss of $23)