Ricardian Model: Production, Opportunity Cost, and Consumption in a Two-Country, Two-Good Economy

To graph Home's production possibility frontier (PPF), we need to plot the combinations of airplanes and cars that Home can produce using its available labor.

The PPF equation for Home can be derived using the production function and the labor constraint:

QA = 1 * LA = LA QC = 5 * LC = 5 * (900 - LA)

Setting QC = 1 and solving for LA, we get:

1 = 5 * (900 - LA) 900 - LA = 1/5 LA = 900 - 1/5 LA = 899.8

So, Home can produce a maximum of 899.8 airplanes and (900 - 899.8) * 5 = 5 cars.

The opportunity cost of airplanes is the amount of cars that Home has to give up to produce one more airplane. In this case, the opportunity cost is the slope of the PPF, which is given by the ratio of the change in cars to the change in airplanes:

Opportunity cost of airplanes = (Change in cars) / (Change in airplanes) = 5 / 1 = 5 cars

In the absence of trade, the price of airplanes in terms of cars would be the same as the opportunity cost, which is 5 cars.

To determine how many airplanes and cars the home country would choose to produce and consume in the absence of trade, we need to find the point on the PPF that maximizes the utility function.

The relative demand function can be derived from the utility function:

(DA/DC) = (MUa/MUc) = (1/3 * DA^(-2/3)) / (2/3 * DC^(-1/3)) = (1/2) * (DA/DC)^(-2/3)

Setting PC = 1, we can rewrite the relative demand function as:

(DA/DC) = (1/2) * (PA/PC)^(2/3)

Since PC = 1, the relative demand function simplifies to:

(DA/DC) = (1/2) * PA^(2/3)

To find the quantities of airplanes and cars that maximize utility, we can set the relative demand function equal to the slope of the PPF:

(DA/DC) = 5

(1/2) * PA^(2/3) = 5

PA^(2/3) = 10

PA = (10^(3/2))^2 PA = 100

Substituting PA = 100 into the PPF equation, we can solve for LA:

QA = LA = 1 * LA = 1 * 900 = 900 airplanes

QC = 5 * LC = 5 * (900 - LA) = 5 * (900 - 900) = 0 cars

Therefore, in the absence of trade, the home country would choose to produce and consume 900 airplanes and 0 cars.