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The economy you described does have a Walrasian Equilibrium when $n$ is even. The Equilibrium price ratio is $\dfrac{p_X}{p_Y}=1$. The corresponding equilibrium allocation is any allocation in which $ …

In the economy you provided, set of feasible allocations is $\mathcal{F}=\{((x_1,y_1),(x_2,y_2))\in\mathbb{R}^2_+\times\mathbb{R}^2_+|x_1+x_2=2 \ \wedge \ y_1+y_2=1\}$ and is represented by points in …

Given an exchange economy: Utility functions: $u_A(x_A,y_A)=\min(x_A,y_A)$, $u_B(x_B, y_B)=\min(x_B, \sqrt{y_B})$ Endowments: $\omega_A = (30,0)$, $\omega_B=(0,20)$ Set of feasible allocations is $\ …

Core Allocations are Pareto efficient allocations that must satisfy individual rationality i.e. these allocations must yield at least as much satisfaction to the individuals as their respective endowm …

Suppose there are two families: Family U has $n_u$ members, and family V has $n_v$ members. Utility function of member $i$ of family U is: \begin{eqnarray*} u_i(x_u, y_u) = a_ix_u + y_u \end{eqnarray* …

Here is another example with two consumers (A and B), two goods (X and Y): \begin{eqnarray*} u_A(x_A, y_A) & = & \min(x_A, y_A), \ \omega_A = (1, 0) \\ u_B(x_B, y_B) & = & \min(x_B, y_B), \ \omega_B …

Given a pure-exchange economy with $u_A(x_A,y_A)=\min(x_A,2y_A)$, $u_B(x_B,y_B)=\min(2x_B,y_B)$ Endowment of A is $(k_X,k_Y)$ and of B is $(12-k_X,12-k_Y)$ Set of feasible allocations is $\mathcal{F …

In the economy provided in the question, competitive equilibrium allocations is equal to the set of efficient allocations. This along with the fact that the competitive equilibrium allocations always …

Set of Pareto Efficient Allocations consists of feasible allocations $((x_J, y_J), (x_D, y_D))$ satisfying $y_J=\displaystyle\frac{x_J}{2}$. Competitive Equilibrium is the price $(p_x, p_y=1)$ sati …

Given a pure exchange economy: $u_A(x_A, y_A)=x_Ay_A$, $u_B(x_B, y_B)=x_By_B^2$ with endowments: $\omega_A=(80,150)$ and $\omega_B=(210,180)$ To find the equilibrium, we first find the price offer cu …

Set of Pareto efficient allocations (or contract curve) is the set of all feasible allocations satisfying $1 \leq x_1=y_1\leq 3$. This is the line segment connecting points A and B in your graph. Also …

In the economy described above, set of efficient allocations is given by the blue curve. Just do the slope of ICs comparisons at the boundaries and you will get that.

Given a pure-exchange economy: $u_1(x_1,y_1)=\max(x_1,y_1)$, $\omega_1=(4,0)$ $u_2(x_2,y_2)=\min(2x_2+y_2,x_2+2y_2)$, $\omega_2=(0,3)$ Set of feasible allocations is given by $\mathcal{F}=\{((x_1,y_ …