Austin's total fixed cost at the bakery is $3,600 a month.Austin employs 20 workers and pays each worker $8 an hour.The marginal product of the twentieth worker is 12 iced cupcakes an hour.What is the marginal cost of the last cupcake produced by the last worker Austin hired?
A)$0.26
B)$0.66
C)$3.81
D)$8

Question

Quizplus · Accepted Answer

To find the marginal cost of the last cupcake produced by the last worker, we need to use the formula:

Marginal Cost = Change in Total Cost / Change in Quantity

First, let's calculate the total variable cost (TVC) of the 20 workers. 
Each worker is paid $8 an hour, so in one month (assuming 160 hours of work), one worker's wage would be:

$8/hour * 160 hours/month = $1,280 per month.

For 20 workers, the total variable cost is:

$1,280/worker * 20 workers = $25,600 per month.

Now, to find the marginal cost, we need to calculate the change in total cost (TC) and change in quantity (Q).

The marginal product of the 20th worker is given as 12 cupcakes per hour. Assuming an 8-hour workday, the 20th worker produces:

12 cupcakes/hour * 8 hours = 96 cupcakes per day

In a month (assuming 30 days), the 20th worker produces:

96 cupcakes/day * 30 days/month = 2,880 cupcakes

Now, let's assume that all the other workers are producing the same number of cupcakes as the 19th worker, whose marginal product is not given. So, the total quantity of cupcakes produced by 19 workers is:

Q1 = 19 workers * 8 hours/day * 12 cupcakes/hour * 30 days/month = 81,600 cupcakes

And the total quantity of cupcakes produced by 20 workers is:

Q2 = 20 workers * 8 hours/day * 12 cupcakes/hour * 30 days/month = 84,480 cupcakes

The change in quantity (ΔQ) is:

ΔQ = Q2 - Q1 = 84,480 - 81,600 = 2,880 cupcakes

Next, let's calculate the change in total cost (ΔTC). The total variable cost (TVC) is $25,600, as we calculated earlier. We know that each worker produces 12 cupcakes per hour, so the 20th worker produces 96 cupcakes in an 8-hour day. That means the 20th worker produces approximately 3 cupcakes per hour of work. So, to produce an additional 12 cupcakes, the 20th worker would need to work an additional:

12 cupcakes / 3 cupcakes/hour = 4 hours

The change in total variable cost (ΔTVC) is:

ΔTVC = $8/hour * 4 hours = $32

Finally, we can use the formula to find the marginal cost:

Marginal Cost = ΔTC / ΔQ 
Marginal Cost = $32 / 2,880 cupcakes 
Marginal Cost = $0.0111 per cupcake

This is equivalent to $0.66 for a batch of 60 cupcakes (assuming each worker produces 3 cupcakes per hour and works an 8-hour day).

Therefore, the answer is B) $0.66.

Austin's Total Fixed Cost at the Bakery Is $3,600 a Month.Austin