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

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

Home's PPF equation is given by: QA = 900/1 = 900 QC = 900/5 = 180

The PPF represents the combinations of airplanes (QA) and cars (QC) that Home can produce. We can plot these values on a graph with airplanes on the x-axis and cars on the y-axis.

The opportunity cost of airplanes is the amount of cars that Home has to give up in order to produce one more airplane. In this case, the 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 the production and consumption quantities in the absence of trade, we need to find the point on the PPF where the relative demand (RD) equals 1. RD is given by:

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

By setting RD equal to 1 and using the PPF equation, we can solve for DA and DC:

(900/4)^(1/3) * (900/2)^(2/3) / (900/1)^(1/3) * (900/5)^(2/3) = 1

Simplifying, we get:

(225/4)^(1/3) * (180)^(2/3) / (900)^(1/3) * (36)^(2/3) = 1

(225/4)^(1/3) * 6 / (900)^(1/3) * 6 = 1

(225/4)^(1/3) / (900)^(1/3) = 1/6

Taking the cube of both sides, we get:

225/4 / 900 = 1/216

Cross multiplying, we get:

225 * 216 = 4 * 900

48600 = 3600

This is not a true statement, so there is no point where RD equals 1. This means that in the absence of trade, Home would not be able to produce and consume both airplanes and cars simultaneously.