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Compute the equilibrium for the two islands

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Reference no: EM13887957

Robinson Crusoe and Friday live on separate islands and produce two goods, cloth yC and food yF using two factors of production, land (T ) and labor (L). The utility functions of both Crusoe and Friday are

u(yF, yC) = yFyC.

The production function for cloth is

yC = 4L1/4T 3/4.

The production function for food is

yF = rL3/4T 1/4.

Crusoe is endowed with two units of labor and one of land. Friday is endowed with one unit of labor and two of land.

(a) Suppose there is no trade between the islands. Compute separate equilibria for Crusoe and Friday, letting the labor of each be the unit of account on his own island.

(b) Suppose there is free trade between the islands in cloth and food but no trade in labor and land. Compute the equilibrium for the two islands together with the labor of Crusoe as the unit of account. (Hint: Use the symmetry of the problem.)

Reference no: EM13887957

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