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Questions and Answers
What is the purpose of elimination of variables in market model problems?
What is the purpose of elimination of variables in market model problems?
In the context of the market model, what indicates that equilibrium quantity $ar{Q}$ will be positive?
In the context of the market model, what indicates that equilibrium quantity $ar{Q}$ will be positive?
If $(b + d) = 0$ in the linear market model, what can be concluded about equilibrium?
If $(b + d) = 0$ in the linear market model, what can be concluded about equilibrium?
What happens to the positions of demand and supply curves if $(b + d) = 0$?
What happens to the positions of demand and supply curves if $(b + d) = 0$?
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Which equation relates demand and supply in a market model?
Which equation relates demand and supply in a market model?
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Study Notes
Market Model Overview
- Market equilibrium occurs when quantity demanded ($Q_d$) equals quantity supplied ($Q_s$).
- Equilibrium prices ($\overline{P}$) and quantities ($\overline{Q}$) are crucial for understanding market dynamics.
Problem 1: Market Model Analysis
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Equations:
- Demand: $Q_d = 24 - 2P$
- Supply: $Q_s = -5 + 7P$
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Elimination Method:
- Set $24 - 2P = -5 + 7P$ to find equilibrium price.
- Solve for $\overline{P}$ and subsequently for $\overline{Q}$.
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Formulas Reference (3.4 and 3.5):
- Specific formulas provide alternative calculations for equilibrium values.
Problem 2: Demand and Supply Function Analysis
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Set (a):
- Demand: $Q_d = 51 - 3P$
- Supply: $Q_s = 6P - 10$
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Set (b):
- Demand: $Q_d = 30 - 2P$
- Supply: $Q_s = -6 + 5P$
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Elimination Method:
- For both sets, equate $Q_d$ and $Q_s$, isolate $P$, then compute $\overline{P}$ and $\overline{Q}$.
Condition for Positive Equilibrium
- For $\overline{Q}$ to be positive, the expression $(ad - bc)$ must share the same sign as $(b + d)$.
- This condition ensures a viable equilibrium exists within the specified market models.
Impact of Zero Sum on Equilibrium
- If $(b + d) = 0$:
- No equilibrium solution can be derived via formulas (3.4) and (3.5) due to the lack of definitive intersection between demand and supply curves.
Graphical Interpretation
- With $(b + d) = 0$, demand and supply curves become parallel, implying no intersection point exists.
- This configuration indicates the absence of equilibrium in the market: sellers and buyers cannot agree on a transaction price.
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Description
Test your understanding of market equilibrium concepts, including demand and supply equations. This quiz will challenge you to analyze different market scenarios using the elimination method to find equilibrium prices and quantities. Gain insights into market dynamics while solving practical problems.
