List of top Microeconomics Questions on General equilibrium and welfare asked in IIT JAM EN

Consider a social welfare function (SWF) defined as \[ SWF=f(U_1,U_2,\ldots,U_m), \] where \(U_i\) is the utility function of the \(i^{th}\) person, given that there are \(m\) people in the society. Identify which one of the following statements is CORRECT.
Which one of the following statements is CORRECT for the general equilibrium analysis for a two-person and two-good pure exchange economy?
Consider a 2-agent, 2-good exchange economy where agent 𝑖 has utility function 𝑢𝑖 (𝑥𝑖 , 𝑦𝑖 ) = max{𝑥𝑖 , 𝑦𝑖 }, 𝑖 = 1,2. The initial endowments of goods 𝑋 and 𝑌 that the agents have are (𝑥̅̅1̅, 𝑦̅̅1̅, 𝑥̅̅2̅, 𝑦̅̅2̅) = (25, 5, 5, 5). Then select the CORRECT choice below where the price vector (𝑝𝑥, 𝑝𝑦) specified is part of a competitive equilibrium.
Consider a 2-agent, 2-good economy with an aggregate endowment of 30 units of good 𝑋 and 10 units of good 𝑌. Agent 𝑖 has utility function
ui (xi , yi ) = max {xi , yi }, 𝑖 = 1, 2. 
Select the choices below in which the specified allocation of the goods to the agents is Pareto optimal for this economy
An economy is characterized by the Solow model, with the production function y = √k, where y is output per worker and k is capital per worker. The steady-state level of output per worker is \(y^{ss}=A^{1/(1-\alpha)}(\frac{\gamma}{\delta})^{\alpha/(1-\alpha)}\) where Α, γ, δ and a denote productivity, share of output invested (in %), depreciation rate (in %) and capital's share in income (in fraction), respectively. Suppose that A = 1, k = 400, \(\gamma\) = 50%, δ = 5% and \(\alpha\)= 1/2. Then the current output, using the above information, is
Which of the following statements is NOT correct under the IS-LM (Fixed Price) model?
Consider a pure exchange economy with two goods x and y. Ravi and Suraj are two individuals with utility functions $U_R = \beta log(xy)$ and $U_s = (x/y)^{\alpha},$ respectively. The endowments are $x_R$ and $y_R$ for Ravi and $x_s$ and $y_s$ for Suraj such that $x_R$+$x_s$ = A and $y_R + y_s= B$. Then their contract curve is