# June 2019, LQ2

## Answer
### c
Let $W_A$ and $W_J$ be the wage rate in the US and Japan, respectively. Let $P_C$ adn $P_T$ be the price of car and truck. By the competitive market, the price should equal to the cost, which is labor input times wage rate.

The price/cost of producing vehicles in the US:

$$
P_C= W_A, P_T= \frac{1}{2} W_A
$$

The price/cost of producing vehicles in the Japan:

$$
P_C= \frac{4}{3} W_J, P_T= W_J
$$

By the free trade, the price of the same good should be equal.

If all firms are producing, we have

$$
\frac{3}{4} W_A= W_J \\
\frac{1}{2} W_A= W_J,
$$

which is impossible.

For the Japanese, making cars can exchange more American labors, in other words, more American goods. Hence, the inefficient Toyota will shut.

### d

Normalize $P_T=1, P_C=P$. Since only Honda works, Japanese's output is $3$ cars and their income is $3P$.

Because the production function is linear, when $P>2$, American will only produce cars; when $P<2$, American will only produce trucks.

By the C-D utility function, everyone should consume both goods. Hence, US cannot specialize on car. (Otherwise, no one produce trucks) And $P<=2$.

Suppose $P<2$, and the US specialize on trucks, then American's output is $8$ trucks, and their income is $8$.

By the C-D utility, American will consume $4$ trucks and $4/P$ cars; Japanese will consume $1.5P$ trucks and $1.5$ cars. By the resource constraint,

$$
4 + 1.5P =8, \frac{4}{P} + 1.5 = 3.
$$

We can solve $P=8/3>2$, which is a contradiction. Hence, the only equilibrium price is $P=2$.

American's income is $4P=8$, Japanese's income is $6$. By C-D utility, US consumes $2$ cars and $4$ trucks; Japan consumes $1.5$ cars and $3$ trucks.

US produces $0.5$ cars and $7$ trucks; Japan produces $3$ cars.