Q.6 (b)Suppose there two goods 1, and 2 with prices p, and p, and the supply and demand functions are specified as follows: S₁ (P₁, P2) == 3p₁; D₁ (P₁, P2)=8-4 P2- P₁ P2 ≤2 and S2 (P1, P2) 5 P2; D2 (P₁, P2) 24-6 p₁- P2, P₁ ≤ 4 The market for good 1 is said to be in equilibrium at prices (p₁, p2°) where S₁ (P₁, P2) = D₁ (P₁, P2°). The market for good 2 is said to be in equilibrium at prices (p₁, p₂) where S₂ (P₁, P₂) =D₂ (P₁, P₂) Demonstrate that each market has equilibrium when the other's price is fixed. Show that nevertheless no pair of prices exists for the two markets at which they are both in equilibrium.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter6: Demand Relationships Among Goods
Section: Chapter Questions
Problem 6.7P
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Q.6
(b)Suppose there two goods 1, and 2 with prices p, and p, and the supply and
demand functions are specified as follows:
S₁ (P₁, P2) == 3p₁;
D₁ (P₁, P2) 8-4 P2- P₁;
P2 ≤2
and
S₂ (P1, P2) - 5 P2;
D₂ (P₁, P2) = 24-6 p₁- P2,
P₁ ≤ 4
The market for good 1 is said to be in equilibrium at prices (p₁, p2°) where
S₁ (P₁, P2°)= D₁ (p₁, p2°). The market for good 2 is said to be in equilibrium at
prices (p₁, p₂) where S₂ (P₁, P₂) =D₂ (P₁, P₂)
Demonstrate that each market has equilibrium when the other's price is fixed.
Show that nevertheless no pair of prices exists for the two markets at which they
are both in equilibrium.
Transcribed Image Text:Q.6 (b)Suppose there two goods 1, and 2 with prices p, and p, and the supply and demand functions are specified as follows: S₁ (P₁, P2) == 3p₁; D₁ (P₁, P2) 8-4 P2- P₁; P2 ≤2 and S₂ (P1, P2) - 5 P2; D₂ (P₁, P2) = 24-6 p₁- P2, P₁ ≤ 4 The market for good 1 is said to be in equilibrium at prices (p₁, p2°) where S₁ (P₁, P2°)= D₁ (p₁, p2°). The market for good 2 is said to be in equilibrium at prices (p₁, p₂) where S₂ (P₁, P₂) =D₂ (P₁, P₂) Demonstrate that each market has equilibrium when the other's price is fixed. Show that nevertheless no pair of prices exists for the two markets at which they are both in equilibrium.
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