Consider an economy where all production and all consumption is carried out by a single agent, Robinson Crusoe. Robinson, as a consumer, is endowed with H hours of time. His utility depends in hours of leisure, h, and coconuts, y: u(h, y) = (h)1−βyβ with 0 ≤ h ≤ H,β ∈ (0,1). Robinson, as a firm, can transform hours of labor, z, into coconuts y. His technology of production is given by y = f(z) = zα with α ∈ (0, 1). Let p denote the price of coconuts, w denote the price of leisure/labor, and π denote the firm’s profits. Note that the budget constraint of Robinson is py ≤ w(H − h) + π. Note that the budget constraint of Robinson is px ≤ w(H − h) + π, and that in equilibrium in the market of coconuts x = y and in the labor market h + z = H. Find the equilibrium allocation and price vector in equilibrium
Consider an economy where all production and all consumption is carried out by a single agent, Robinson Crusoe. Robinson, as a consumer, is endowed with H hours of time. His utility depends in hours of leisure, h, and coconuts, y: u(h, y) = (h)1−βyβ with 0 ≤ h ≤ H,β ∈ (0,1). Robinson, as a firm, can transform hours of labor, z, into coconuts y. His technology of production is given by y = f(z) = zα with α ∈ (0, 1). Let p denote the price of coconuts, w denote the price of leisure/labor, and π denote the firm’s profits. Note that the budget constraint of Robinson is py ≤ w(H − h) + π. Note that the budget constraint of Robinson is px ≤ w(H − h) + π, and that in equilibrium in the market of coconuts x = y and in the labor market h + z = H. Find the equilibrium allocation and price vector in equilibrium
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider an economy where all production and all consumption is carried out by a single agent, Robinson Crusoe. Robinson, as a consumer, is endowed with H hours of time. His utility depends in hours of leisure, h, and coconuts, y: u(h, y) = (h)1−βyβ with 0 ≤ h ≤ H,β ∈ (0,1). Robinson, as a firm, can transform hours of labor, z, into coconuts y. His technology of production is given by y = f(z) = zα with α ∈ (0, 1). Let p denote the price of coconuts, w denote the price of leisure/labor, and π denote the firm’s profits. Note that the budget constraint of Robinson is py ≤ w(H − h) + π. Note that the budget constraint of Robinson is px ≤ w(H − h) + π, and that in equilibrium in the market of coconuts x = y and in the labor market h + z = H. Find the equilibrium allocation and price vector in equilibrium.
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