Question

Japanese labor productivity is roughly the same as that of the US in the manufacturing sector, while the US is more productive in the service sector. But most services are non-tradable. Some have argued that this poses a problem for the US, because US’s comparative advantage lies in things US cannot sell on world markets. ” To evaluate this statement, develop a small Ricardian model: Suppose that Japan has roughly half the population of the United States, so set L= 10 and L∗= 5. Suppose there are two manufacturing sectors (i.e., cars and electronics), and a non-tradable service sector. Suppose that the technologies have labor productivity of one in all sectors for Japan. Let the US have a labor productivity for manufacturing sectors of one as well, and a productivity of services of 3. Let utility be Cobb-Douglas, with a share of expenditure on cars and electronics of 0.25 each,and a share of expenditure on services of 0.5. Suppose there are extremely small trade costs between countries, which you normally ignore, but in case of indifference between home and foreign sourcing in the absence of trade costs, the good will be bought from home. Trade costs are infinite for services. 1. Solve the model, e.g., derive results for production, consumption, wages, and prices in each country and calculate welfare in each country. 2. Now assume that the US had a labor productivity in services and cars of 1, but a labor productivity in electronics of 3. Again, solve the model, e.g., derive results for production, consumption, wages, and prices in each country and calculate welfare in each country. 3. Use your results from the previous to steps to comment on the statement made at the beginning of this question.

Answer 1

Answer:

It is given to us that labor in US is 30, L= 30 and labor in Japan is 10, L* = 10. It is also given to us that Japan has a labor productivity of 1 in all sectors while US has labor productivity of 1 in manufacturing and 2 in services sector. With this information we can see the comparative advantage of each country in each product, manufacturing and services.

1. Assume PrLM = 1 is the labor productivity in manufacturing in US while PrLS = 2 is the labor productivity in services in US. Pr*LM = 1 is the labor productivity in manufacturing in Japan while Pr*LS = 1 is the labor productivity in services in Japan.

To find the comparative of manufacturing sector in both countries, we calculate :

3 x (PrLM/PrLS) = 3 (1/2) = 3 x0.5 = 1.5 (we multiply the productivity by 3 as US has 3 times the labor as Japan)

Pr*LM/Pr*LS = 1/1 = 1

Since productivity is more in US because 1<1.5, US has a comparative advantage over Japan in the manufacturing sector.

To find the comparative of services sector in both countries, we calculate :

3 x (PrLS/PrLM) = 3 x (2/1) = 6

Pr*LS/Pr*LM = 1/1 = 1

Since productivity is more in US because 1<6, US has a comparative advantage over Japan in the services sector as well.

However, since services are a non-tradable good, it will produced and consumed equally in both countries.

Now, we have also been given the cobb douglas utility function :

U (M,S) = U(M0.5S0.5)

Where M and S denote consumption of manuacturing and services.

It is given to us that the share of expenditure/consumption on cars is 0.15 and that on services is 0.7. The productivity in japan is 1. So utility in Japan will be

= U(0.15)1(0.7)1

= 0.105

The productivity in US is 1 in manufacturing and 2 in services. So utility in US will be :

U(M,S) = U(0.15)1(0.7)2

= 0.15 x 0.49

= 0.073

Clearly, the utility is higher in Japan, despite having fewer labor.

2. Now, if PrLM = 2 is the labor productivity in manufacturing in US while PrLS = 1 is the labor productivity in services in US. Pr*LM = 1 is the labor productivity in manufacturing in Japan while Pr*LS = 1 is the labor productivity in services in Japan.

To find the comparative of manufacturing sector in both countries, we calculate :

3 x (PrLM/PrLS) = 3 (2/1) = 6 (we multiply the productivity by 3 as US has 3 times the labor as Japan)

Pr*LM/Pr*LS = 1/1 = 1

Since productivity is more in US because 1<6, US has a comparative advantage over Japan in the manufacturing sector.

To find the comparative of services sector in both countries, we calculate :

3 x (PrLS/PrLM) = 3 x (1/2) = 3 x 0.5 = 1.5

Pr*LS/Pr*LM = 1/1 = 1

Since productivity is more in US because 1<1.5, US has a comparative advantage over Japan in the services sector as well.

However, since services are a non-tradable good, it will produced and consumed equally in both countries.

Now, we have also been given the cobb douglas utility function :

U (M,S) = U(MaSb)

Where M and S denote consumption of manuacturing and services.

It is given to us that the share of expenditure/consumption on cars is 0.15 and that on services is 0.7. The productivity in japan is 1. So utility in Japan will be

= U(0.15)1(0.7)1

= 0.105

The productivity in US is 2 in manufacturing and 1 in services. So utility in US will be :

U(M,S) = U(0.15)2(0.7)1

= 0.022 x 0.7

= 0.01

Here too, the utility is higher in Japan, despite having fewer labor. In this case, utility in US slips further.

3. Given, the calculations, the statement in the question cannot be made as not all the information has been collected to make a statement on the comparative advantage of each country. Eventhough the calculations above show comparative advantage of US in both sectors on account of higher labor supply, it does not indicate an actual comparative advantage. This is because labor in a country will be divided among the sectors and will not be wholly involved in one sector or the other. Also, to determine comparative or absolute adavantage both relative productivity