Question

In: Economics

Two countries produce two different items, root beer and cheese. The table below shows the amounts...

Two countries produce two different items, root beer and cheese. The table below shows the amounts of each commodity that each country can produce with 400 units of factor inputs (productive units). Before trade consumption in each country is equal to production – that is, if trade is warranted, citizens need to receive at least as much root beer and cheese as they started with before trade. Given the following production levels, calculate the best possible trading scenario that maximizes production in this two-country world. Remember each country has 400 productive units which they can use in any combination. Before trade, each country has allocated 50% of their productive units to each product. That is, before trade, Hokieland makes 100 gallons of root beer and 20 wheels of cheese. Based on the theory of Comparative Advantage, what should each country do if they trade? [be careful, you need to make at least as much of each output after trade as you had before trade.] Explain your solution. Use this example to clearly explain the difference between Absolute and Comparative advantage. Bold the Solution

Hokieland Eagleland
Root beer 2 units per gallon 4 units per gallon
Cheese 5 units per wheel 8 units per wheel

Solutions

Expert Solution

Hokieland used 2 units of input to produce a gallon of root beer and 5 units of input to produce a wheel of cheese.

Eagleland used 4 units of input to produce a gallon of root beer and 8 units of input to produce a wheel of cheese.

let's see which country produces how much if they choose to use all factor inputs in 1 commodity.

Hokieland Eagleland
Root beer 200 gallons 100 gallons
Cheese 80 wheels 50 wheels

We can see that Hokieland produces more beer and cheese than Eagleland so Hokieland has an absolute advantage in producing beer and cheese

Now let's look at the opportunity cost of both countries in producing each product.

To produce each gallon of beer, Hokieland has to sacrifice 80/200 = 0.4 units of cheese while Eaglelend has to sacrifice 50/100 = 0.5 units of cheese. So here, Hokieland has a comparative advantage over Eagleland as it has to sacrifice less of its cheese to make beer. So Hokieland will trade in beer

To produce each wheel of cheese, Hokieland has to sacrifice 200/80 = 2.5 gallons of beer and Eagleland has to sacrifice 100/50 = 2 gallons of beer. Here, Eagleland has a comparative advantage over Hokieland as it has to sacrifice less of its beer to make cheese. So Eagleland will trade in cheese.

Hokieland Eagleland
Root beer 0.4 cheese 0.5 cheese
Cheese 2.5 2

Before the trade, the consumption and production patterns looked like this. The uppermost table shows how much they could produce if they put all their resources into one product

hokieland Eaglelend
root beer 100 50
Cheese 40 25

If they want to trade to increase the consumption of their citizens, They both need to produce at least 150 gallons of root beer and 65 wheels of cheese. Now Hokieland can produce beer for both countries but Eagleland cannot produce enough cheese for both of them so Hokieland will have to produce some cheese for itself also.

Eagle land can produce 50 wheels of cheese but only needs 25, say they sell 24 wheels and keep 26 for themselves at the rate of 2.2 gallons of beer per wheel. At that rate, they will get 52.8 gallons of beer which is more than what they used to consume i.e 50 gallons

Hokieland can produce 17 wheels of cheese for itself and hence will have 17 + 24 = 41 cheese wheels. To make 17 wheels of cheese, it has to sacrifice 17 * 2.5 = 42.4 gallons of beer. So now it can only produce 157.5 gallons of beer. It will sell 52.8 gallons to Eagleland and now will have 104.7 gallons of beer for themselves.

below is the production of both countries

hokieland Eaglelend
root beer 157.50 0.00
Cheese 17.00 50.00

Consumption of both is given as:

hokieland Eaglelend
root beer 104.70 52.80
Cheese 41.00 25.00

As one can see, everyone won in this situation, by using the concept of comparative advantage.


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