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Robinson Crusoe Economy Question

If you want to find Pareto efficient allocation in this economy, then you can determine that by solving the following system for $(C, L, H)$: $L+H=1$ $C = 8\sqrt{H}$ $\text{MRS} = \dfrac{3C}{2L} = \...
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How to find a Walrasian equilibrium for this production economy?

Solving the profit maximisation problem of firm producing $x$, $\max_{x\geq 0, l_X\geq 0} \ p_Xx - l_X$ subject to $x = 2\sqrt{l_X}$ gives the demand for labor by firm producing $x$ and supply of $x$ ...
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How to show there is no a Walrasian equilibrium?

Given the exchange economy, Three Goods: X (Apple), Y (Banana), M (Money) Three Agents: Seller (S), Buyer 1 (A), Buyer 2 (B) Endowment of the seller: $W_S=(1,1,0)$; Endowment of the buyers: $W_A=W_B=(...
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Exchange economy with trade

First, let us observe the autarky equilibrium: Consumer $0$'s utility maximisation problem is $\displaystyle\max_{x_0\geq 0,y_0\geq 0}x_0^\alpha y_0^{1-\alpha}$ subject to $px_0+y_0\leq p$ Solving it ...
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Solve for the Walrasian demand, Utility of three variables, and Convexity of Preferences?

$u(x,y,z)=x^{\frac{2}{3}}y^{\frac{1}{3}}+z$ is the sum of two concave functions: $u_1(x,y,z)=x^{\frac{2}{3}}y^{\frac{1}{3}}$ and $u_2(x,y,z)=z$, and therefore, it is concave. Since $u$ is concave, it ...
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Perfect Complements - Walrasian Equilibrium

Set of feasible allocations is $\mathcal{F}=\{((a_1,b_1),(a_2,b_2))\in\mathbb{R}^2_+\times\mathbb{R}^2_+|a_1+a_2=30 \ \wedge b_1+b_2=20\}$ As can be seen from the picture below, set of competitive ...
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