Answer the following questions in about 150 words each: (a) Compare and contrast Marshallian and Walrasian approaches of the…

(a) Marshallian and Walrasian stability. Marshallian stability is a partial-equilibrium test. In one market, price adjusts to excess demand: if demand exceeds supply, price rises; if supply exceeds demand, price falls. Formally, dp/dt = λD(p), with λ>0; equilibrium is locally stable when the excess-demand curve cuts the price axis from above, so a small price deviation generates a restoring force. The analysis holds other prices fixed and assumes the market can clear independently. Walrasian stability is a general-equilibrium test. All commodity prices adjust simultaneously through a tâtonnement process, with no trade off equilibrium. The vector of excess demands Z(p) determines dp/dt, and stability requires that the system of price equations converge to p* from nearby initial prices; locally this requires the eigenvalues of the excess-demand Jacobian to have negative real parts. The contrast is therefore between one-price, market-by-market adjustment and all-price, system-wide adjustment, with different assumptions about speed and interdependence.

(b) Generalised Lorenz dominance and welfare. The Lorenz curve plots cumulative income share against cumulative population share; the generalized Lorenz curve multiplies it by mean income μ, so G(p)=μL(p). Distribution A dominates B by generalized Lorenz dominance if G_A(p)≥G_B(p) for all p, with strict inequality somewhere, implying a higher or equal mean and no crossing. This dominance is welfare-relevant because any social welfare function that is increasing in income, symmetric, and concave (inequality-averse) ranks A at least as high as B. Atkinson’s theorem formalises this: for a given inequality-aversion parameter ε, welfare can be written as μ(1-I(ε)), where I(ε) is the Atkinson index; a higher generalized Lorenz curve lowers I(ε) and raises welfare. Thus, at the same mean, a lower-inequality distribution has a higher Lorenz and generalized Lorenz curve and yields higher welfare for all inequality-averse preferences; if it also has a higher mean, the welfare gain is unambiguous. Hence lower inequality, when it does not reduce the mean, represents a higher social welfare state.

(c) Business cycle and autonomous expenditure. Autonomous expenditure Aₜ is the impulse that starts a cycle. In the Samuelson-Hicks linear model, output is Yₜ=Cₜ+Iₜ+Aₜ, with consumption Cₜ=cYₜ₋₁ and investment Iₜ=v(Yₜ₋₁-Yₜ₋₂). Substitution gives Yₜ=(c+v)Yₜ₋₁-vYₜ₋₂+Aₜ. A rise in Aₜ raises income through the multiplier, 1/(1-c), while the accelerator makes investment respond to the change in output, so the initial demand shock is amplified and fed back into later periods; a fall in Aₜ reverses the process. The homogeneous characteristic equation is λ²-(c+v)λ+v=0. When (c+v)²<4v, the roots are complex and output fluctuates cyclically; the modulus of the roots determines whether cycles are damped, constant, or explosive. If roots are real, adjustment is monotonic or non-cyclical. Because the model is linear, the amplitude is proportional to the autonomous shock, and cycles arise from parameter values rather than non-linearity. Thus autonomous expenditure changes are the exogenous trigger, while the multiplier-accelerator interaction converts them into business-cycle dynamics.

(d) Crowding out. Government borrowing does not always crowd out private investment. In the IS-LM framework, a deficit-financed rise in government spending shifts IS right; if the LM curve is upward sloping, the new equilibrium has a higher interest rate, which reduces private investment. The size of crowding out depends on the slope of LM and the interest sensitivity of investment. With a vertical LM curve, the interest rate rises enough to offset the entire increase in government spending, giving full crowding out. With a horizontal LM curve, as in a liquidity trap, the interest rate does not rise, so crowding out is minimal. In a recession with idle capacity, public investment can also crowd in by improving infrastructure, raising expected returns, or increasing confidence. Ricardian equivalence offers a further qualification: if households anticipate future taxes and save more, borrowing may not raise interest rates. Hence crowding out is a tendency, not an identity; it is strongest near full employment and tight monetary conditions, as when market borrowings tighten liquidity. In India, RBI liquidity conditions shape this effect.

(e) IS slope and taxes. True in the algebraic IS equation, where slope is the income response to interest-rate changes. Let C=a+c(Y-T), T=T0+tY, and I=I0-br. Then Y=a+c(Y-T0-tY)+I0-br+G, so Y[1-c(1-t)]=a-cT0+I0+G-br. Hence dY/dr=-b/[1-c(1-t)]. A reduction in the proportional tax rate t lowers 1-c(1-t), raising the absolute value of dY/dr and increasing the multiplier 1/[1-c(1-t)]; the IS schedule therefore becomes steeper in the Y-r algebra. A reduction in lump-sum tax T0 changes only the intercept a-cT0+I0+G, shifting IS without altering dY/dr. In the conventional r-Y diagram, the same algebra is drawn as a flatter IS, but the statement’s slope claim is correct when slope is the coefficient of r in the income equation.