Ricardian Model with Two Countries: Production, Opportunity Cost, and Consumption

To graph Home's production possibility frontier, we need to determine the maximum amount of airplanes and cars that Home can produce given its resources.

The production possibility frontier is given by the equation:

DA * aLA + DC * aLC = total labor

Substituting the given values, we have:

DA + 5DC = 900

To find the maximum amount of airplanes Home can produce, we set DC to 0 and solve for DA:

DA = 900

To find the maximum amount of cars Home can produce, we set DA to 0 and solve for DC:

5DC = 900 DC = 180

Therefore, Home's production possibility frontier is a straight line connecting the points (900, 0) and (0, 180).

The opportunity cost of airplanes is the amount of cars Home must give up in order to produce one more airplane. From the production possibility frontier, we can see that Home's opportunity cost of airplanes is 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 Home would choose to produce and consume in the absence of trade, we look at the point on the production possibility frontier that maximizes Home's utility.

Home's utility function is U(DA, DC) = DA^(1/3) * DC^(2/3).

To maximize utility, we need to find the combination of airplanes and cars that maximizes U(DA, DC) while still satisfying the production possibility frontier equation.

Using calculus, we can find the maximum by taking partial derivatives with respect to DA and DC, setting them equal to zero, and solving for DA and DC.

∂U/∂DA = (1/3) * DA^(-2/3) * DC^(2/3) = 0 ∂U/∂DC = (2/3) * DA^(1/3) * DC^(-1/3) = 0

Solving these equations, we find DA = 0 and DC = 0, which means that without trade, Home would not produce or consume any airplanes or cars.