Loco Pony Adventures rents clowns and ponies for children's birthday parties

Accounting Dec 09, 2020

Loco Pony Adventures rents clowns and ponies for children's birthday parties. If the annual total cost of furnishing entertainment is given by TC = 0.5Q2 + 25Q + 1,000, the average variable cost of catering to 30 birthday parties is

Expert Solution

The total cost is calculated as:

TC=FC+VCTC=FC+VC

Given the total cost function:

TC=0.5Q2+25Q+1,000TC=0.5Q2+25Q+1,000

The fixed cost will be determined when Q = 0.

FC=TC(0)=1,000FC=TC(0)=1,000

Therefore, the variable cost will be equal to:

VC=TC−FC=0.5Q2+25Q+1,000=1000=0.5Q2+25QVC=TC−FC=0.5Q2+25Q+1,000=1000=0.5Q2+25Q

The variable cost of catering to Q = 30 birthday parties is equal to:

VC=0.5(30)2+25(30)=$1,200VC=0.5(30)2+25(30)=$1,200

Thus, the average variable cost of catering for 30 birthday parties is equal to:

AVC=VCQ=120030=$40AVC=VCQ=120030=$40 per birthday party.

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