Walrasian General Equilibrium | Microeconomics | Dec 2023 | NTA UGC NET Economics | Kiranraj - Apple B UGC NET JRF Academy

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Walrasian General Equilibrium | Microeconomics | Dec 2023 | NTA UGC NET Economics | Kiranraj

What is Walras’ Law?

Walras’ Law states that in an economy with n markets, if n − 1 markets are in equilibrium, then the nth market must also be in equilibrium, as long as agents obey their budget constraints.

Where:

  • Pi​ is the price of good i,
  • Ei is the excess demand for good i (demand minus supply).

Thus, the total value of excess demand across all markets is zero.

Walras’ Law

  • Every consumer and producer faces a budget constraint.
  • If someone is demanding more of one good than is supplied (excess demand), they must be supplying more of something else (excess supply) to pay for it.
  • The market doesn’t allow you to be in net excess demand for everything.

Walras’ Law

  • Imagine you’re at a huge market with n different stalls: one sells apples, another sells shirts, another sells books, and so on.
  • Now think of everyone in this market: people can only spend what they earn or have — no magic money. That’s their budget constraint.
  • If n − 1 of those stalls (markets) are working just fine — meaning everything people want to buy and sell matches up — then the last stall will also balance out, automatically.

Example:

If you want :

  •  More apples than are available (excess demand for apples),
  • But you’re selling extra books (excess supply of books),
  •  Your money situation stays the same (money market in balance).
  • Because you’re offering more books, you can afford to want more apples. That balances things out.
  • So if the book and money markets are in balance, the apple market must be too — the math of your budget makes it happen.

Walras’ Law and the Walrasian Demand Function

Budget Exhaustion (Walras’ Law at the micro level) :

  •  P⋅X(P,W)=W→ Consumers fully exhaust their wealth.
  • The total value of what the consumer demands equals their wealth. In words: you spend all your money.

Homogeneity of Degree Zero

  •  The demand function X(P,W)is homogeneous of degree zero in P and W. This means:
  • X(αP,αW)=X(P,W)→ If all prices and income change by the same proportion, your real purchasing power is unchanged, so your consumption bundle stays the same.

Continuity & Walrasian Consistency

  • The Walrasian demand function is usually assumed to be continuous, single-valued, and satisfying Walras’ Law.
  • Ensures general market consistency → If all but one market clear, the last must as well.

2023 JUNE

Which of the following is are correct about Walrasian demand function?

a. The Walrasian demand function X (P, W) is homogeneous of degree zero if X (αP, αW) = X (P, W) for any P, W and α > 0.

b. The Walrasian demand function X (P, W) is homogeneous of degree one if X (αP, αW) = αX (P, W) for any P, W and α > 0.

c. The Walrasian demand function X (P, W) satisfies Walras’ law if for every P >> 0 and W > 0, we have P × X = W, for all A ∈ X (P, W).

d. Walras’ law says consumer fully expends his wealth.

e. If price and wealth both change in same proportion, then individual consumption choice does not change.

Option

Choose the collect answer from the option given below : 

A. a, b, c, d only 

B. b, c, d, e only

C. a, b, c, e only 

D. a, c, d, e only 

(a) “X(P, W) is homogeneous of degree zero if X(αP, αW) = X(P, W)“

Walrasian demand is homogeneous of degree zero in prices and wealth, meaning if prices and wealth change by the same proportion, demand doesn’t change.

(b) “X(P, W) is homogeneous of degree one if X(αP, αW) = αX(P, W)”

  • This is the definition of homogeneity of degree one, but Walrasian demand is not degree one — it is degree zero.

(c) “X(P, W) satisfies Walras’ Law : P · X(P, W) = W”

Core of Walras’ law: the value of demand equals the consumer’s wealth (i.e., The consumer fully spends their budget).

(d) “Walras’ law says consumer fully expends his wealth.”

Budget Exhaustion (Walras’ Law at the micro level) :

✔️ P⋅X(P,W)=W→ Consumers fully exhaust their wealth.

✔️ The total value of what the consumer demands equals their wealth. In words: you spend all your money.

(e) “If price and wealth both change in same proportion, consumption doesn’t change.”

✔️ The demand function X(P,W)is homogeneous of degree zero in P and W. This means:

✔️ X(αP,αW)=X(P,W)If all prices and income change by the same proportion, your real purchasing power is unchanged, so your consumption bundle stays the same.

  1. a, c, d, e only 

 

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