Question

Suppose you own an outdoor recreation company and you want to purchase all-terrain vehicles (ATVs) for your summer business and snowmobiles for your winter business. Your budget for new vehicles this year is $240,000. ATVs cost $8000 each and snowmobiles cost $12,000 each.

a.Draw a budget line for your purchase of new vehicles.

b. What is the opportunity cost of one ATV?

c. What is the opportunity cost of one snowmobile?

Answer 1

Step 1: find the LCM of the cost of ATV and Snowmobile:

8000 = 4 x 2 x 1000

12000 = 4 x 3 x 1000

So 4 x 3 x 2 x 1000 = 24000

Step 2: Divide the investment by the cost of 1 ATV to find the maximum number of ATVs that can be purchased:

240000/8000 = 30 ATVs

Step 3: Divide the LCM by cost of Snowmobile to find out how many snowmobiles can be bought

24000/12000 = 2 Snowmobiles

Step 4: Divide the LCM by cost of ATV to find out how many ATV can be sacrificed

24000/8000= 3 ATVs

Step 5: For every 2 snowmobiles to be purchased we will have to sacrifice 3 ATVs Using this develop a schedule for number of ATVs and Snowmobiles:

ATV	Snowmobile	Cost of ATV	Cost of Snow mobile	Total investment
30	0	30x8000=240000	0x12000=0	240000
27	2	27x8000=216000	2x12000=24000	216000+24000=240000
24	4	24x8000=192000	4x12000=48000	19200+48000=240000
21	6	21x8000=168000	6x12000=72000	168000+72000=240000
18	8	18x8000=144000	8x12000=96000	144000+96000=240000
15	10	15x8000=120000	10x12000=120000	120000+120000=240000
12	12	12x8000=96000	12x12000=144000	96000+144000=240000
9	14	9x8000=72000	14x12000=168000	72000+168000=240000
6	16	6x8000=48000	16x12000=192000	48000+192000=240000
3	18	3x8000=24000	18x12000=216000	24000+216000=240000
0	20	0x8000=0	20x12000=240000	240000

Opportunity cost of ATV: To produce 3 ATV we need to give up producing 2 Snow mobile, so opportunity cos per unit of ATV = 2/3=0.667 Snowmobiles

Opportunity cost of Snowmobile: To produce 2 Snowmobile we need to give up producing 3 ATV, so opportunity cos per unit of ATV =3/2=1.5 ATV