I just need c. Authorities from New Zealand have outlawed the export of koalas t

Question

I just need c.

Authorities from New Zealand have outlawed the export of koalas to zoos and an illegal market for koalas has since developed. The cost of capturing a koala and shipping it to the United States (US) is roughly $d per, and smuggled koalas are drugged and shipped in suitcases. This experience is highly traumatic for the koalas and 60% of them die in transit. Each smuggled koala has a 15% chance of being discovered in the US, in which case the koala is confiscated and a fine of $F per koala is charged. All confiscated and deceased koalas are returned to New Zealand. What is the probability that a smuggled koala will reach the buyer alive? If the price of a smuggled koala is p, what is the expected gross revenue to the koala smuggler from shipping one koala? What is the expected gross revenue from shipping q koalas? What is the expected cost, including expected fines and the cost of capturing and shipping per koala? At what price does a koala smuggler break even? Call this price, P_b. How does p_b change when F changes? If the demand for koalas per year is q = 7200 - 10p and F = 250 and d = 20, how many koalas will be sold in the US per year at p_b? How many koalas must be caught in New Zealand in order that this number of koalas reaches US buyers? Suppose demand for koalas per year is q = 7200 - 10p. the fine is again F (not $250), and there is only one koala smuggler. How many koalas will be sold in the US per year? How would your answer to (e. i) change if the fine were not per koala but was instead a lump sum fine (i.e., was $F regardless of how many koalas beyond one were confiscated)? Explain the differences in your answers to (e. i) and (e. ii) using your intuition.

Explanation / Answer

Solution to part c.:

Breaking even means:

The point at which cost and income are equal,

that is there neither profit nor loss.

Here the breaking even cost is denoted,as per the problem, by : pb.

The smuggler breaking even at pb would simply mean

that at this price, if the koalas were shipped,then it would cover exactly the total cost incurred in the whole process of the trading.

Important: The cost of capturing and shipping is the cost incurred by the smuggler,not a profit. It is an expense on the part of the smuggler,not a revenue!

What else might be the cost incurred by the smuggler? : 1. The cost of death of koala

2. The cost of getting fined.

Note that,if 100 koalas are smuggled,then the smuggler would expect a revenue or profit over all these 100 koalas,(this is the basic, as none of the koalas have died or have been fined for,yet.)

Cost of capturing and shipping /koala: d$

So ,total cost of shipping 100 koalas = 100*d $

Next, we have been informed that 60% of the koalas die in the transit,

so: out of 100 koalas, 40 remain.

Now,next,each smuggled koala has a 15% chance of getting discovered,and hence fined for.

So, out of the remaining 40 koalas, number of koalas that would be fined for are: 15/100*40= 6

So,total cost of fine= 6*F $

Important: Originally,the smuggler would account for 100 koala bears, but now he accounts just for (40-6)=34 koala bears. ( After death of 60% of 100 koala bears,40 remain, and out of them 6 are confiscated, so : 40-6)

So,originally he would want to have profit over 100 koalas he smuggled,
but now,he has only 34 koalas to rely on.

So ,total cost incurred by smuggler=( Cost for shipping and capturing+ Fine incurred)

=(100*d+6*F)$

To break even, pb should be equal to= (100*d+6*F)/34 per koala.

Thus,pb= (100*d+6*F)/34 per koala.

At this price per koala,the smuggler breaks even.

Also , as per the equation,
as F increases, pb increases,id d is kept constant.

pb varies directly with F.

***********************************************

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---