Question

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Randy and Frank are both landscapers. Randy can mow 8 lawns per day or prune 12 trees. Frank can mow 10 lawns per day or prune 20 trees. Randy and Frank each work 240 days per year. a. Determine who has the absolute advantage at each task, what their respective opportunity costs are for mowing a lawn, and who has comparative advantage in each task. Frank has an absolute advantage in mowing lawns. Frank has an absolute advantage in pruning trees. Instructions: Round your answers to two decimal places. The opportunity cost of mowing a lawn for Randy is 15 trees. The opportunity cost of mowing a lawn for Frank is trees. Randy has a comparative advantage in mowing lawns. Frank has a comparative advantage in pruning trees. b. Assuming that only one of the tasks is performed, then together Randy and Frank can service a maximum of trees each year. lawns or c. If each landscaper fully specializes according to his comparative advantage, then the maximum number of lawns that can be mowed annually is and the maximum number of trees that can be pruned is per year.

Answer 1

(a)

Randy can mow 8 lawns per day while Frank can mow 10 lawns per day.

It can be seen that Frank can mow more lawns per day.

So,

Frank has an absolute advantage in mowing lawns.

Randy can prune 12 trees in a day while Frank can prune 20 trees in a day.

It can be seen that Frank can prune more trees in a day.

So,

Frank has an absolute advantage in pruning trees.

Randy can mow 8 lawns per day or prune 12 trees

Thus,

The opportunity cost of mowing a lawn for Randy is (12/8) 1.5 trees.

Frank can mow 10 lawns per day or prune 20 trees

Thus,

The opportunity cost of mowing a lawn for Frank is (20/10) 2 trees.

It can be seen that Randy can mow lawns at lower opportunity cost relative to Frank.

so,

Randy has a comparative advantage in mowing lawns.

Frank has a comparative advantage in pruning trees.

(b)

Randy can mow 8 lawns per day while Frank can mow 10 lawns per day.

So, collectively, they can mow 18 lawns per day.

Each year, they work for 240 days.

Total lawns mowed = 18 * 240 = 4,320 lawns

Randy can prune 12 trees per day while Frank can prune 20 trees per day.

So, collectively, they can prune 32 trees per day.

Each year, they work for 240 days.

Total trees pruned = 32 * 240 = 7,680 trees

So,

Together Randy and Frank can service a maximum of 4,320 lawns or 7,680 trees each year.

(c)

Randy can specialize in mowing lawns. It ca mow 8 lawns per day. So, in 240 days, it can mow (240 * 8) 1,920 lawns.

Frank can specialize in pruning trees. It can prune 20 trees per day. So, in 240 days, it can prune (240 * 20) 4,800 lawns.

So,

If each landscaper fully specializes according to his comparative advantage, then the maximum number of lawns that can be mowed annually is 1,920 and the maximum number of trees that can be pruned is 4,800 per year.