(UPSC Economics Optional 2014) Question 6:

Discuss the cobweb model of dynamic equilibrium with lagged adjustment. Explain how the existence of a stable equilibrium depends on the nature of the demand and supply curves. (20 marks)

Part one:
Dynamic Stabiltiy: Dynamic stability considers how price and quantity change through time when the system is thrown into a disequilibrium state. Dynamic analysis of stability investigates the time path of the adjustment process of the movement of price and quantity towards the equilibrium levels.

Equilibrium is stable in the dynamic sense if the price converges to the equilibrium price, unstable otherwise.

Dynamic stability with lagged cobweb model:

Time lag and Supply lag: There exists lag between adjustment of price to supply.

St = f(Pt-1)
Dt = St
St = gPt-1 + c

Damped oscillation and Stable Dynamic Equilibrium:

The cobweb model is based on a time lag between supply and demand decisions.

The above figure represents the convergent case: each new outcome is successively closer to the intersection of supply and demand.

Explosive Oscillations and Unstable equilibrium:
The above figure represents The divergent case: each new outcome is successively further from the intersection of supply and demand.


Perpetual Oscillations - Don't move towards  equilibrium:

Part Two:

Existence of a stable equilibrium depends on the nature of the demand and supply curves
The cobweb model can have two main types of outcomes:

• If the supply curve is steeper than the demand curve, then the fluctuations decrease in magnitude with each cycle, so a plot of the prices and quantities over time would look like an inward spiral, as shown in the first diagram. This is called the stable or convergent case.
• If the slope of the supply curve is less than the absolute value of the slope of the demand curve, then the fluctuations increase in magnitude with each cycle, so that prices and quantities spiral outwards. This is called the unstable or divergent case.