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The consumer then faces the budget constraint wR + c = Y = o + 168w. Each budget-isoprofit line has slope −w. Walras’s Law results from subtracting the right-hand side of this expression from the left. 31) where w is the wage rate in oysters per labor-hour, Ld is labor demanded, R is leisure demanded, q s = F (Ld ) is oyster supply, and c is oyster demand. 3 Define fully a general competitive equilibrium. What does equilibrium require for w? What is required of c, R, q, and L? Clearly describe firm behavior, household behavior, and market-clearing conditions.

Note the decentralization of the decision process here: The firm chooses L and q; the household chooses c and R. Only in equilibrium will the separate decisions be consistent with one another. Consistency requires q = c and R = 168 − L. 23). 23). It is not an equilibrium condition because it is true both in and out of equilibrium. It does summarize two observations, (1) that household income is sufficient to purchase total economic output and (2) that in an economy of scarcity, all income will be spent.

Robinson is the sole owner of the oyster harvester, so he includes profits of the oyster firm as part of his income. A simplifying convention is to treat Robinson’s labor income as the value of all of his labor. This amounts to the (awkward) usage that he sells all of his labor on the market and then buys most of it back as leisure. 7) are known as first-order necessary conditions for an interior maximum. Combined with the concavity properties assumed for F (·) and u(·) (second-order conditions), they ensure a utility maximum subject to constraint.

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