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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?
- To visualize demand and supply curves.
- To derive supply and demand functions from observations.
- To test the robustness of the model against variances.
- To find the equilibrium price and quantity. (correct)
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?
- There must be a consistent increase in supply with price.
- The demand function must intersect the x-axis.
- The supply function needs to extend beyond the demand function.
- The expression $(ad - bc)$ must have the same sign as $(b + d)$. (correct)
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?
- The model is invalid and cannot provide an equilibrium solution. (correct)
- Prices will adjust indefinitely without stabilizing.
- An equilibrium cannot exist as demand equals zero.
- An equilibrium exists at negative price levels.
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
- Equations:
- Demand: $Q_d = 24 - 2P$
- Supply: $Q_s = -5 + 7P$
- Elimination Method:
- Set $24 - 2P = -5 + 7P$ to find equilibrium price.
- Solve for $\overline{P}$ and subsequently for $\overline{Q}$.
- Formulas Reference (3.4 and 3.5):
- Specific formulas provide alternative calculations for equilibrium values.
Problem 2: Demand and Supply Function Analysis
- Set (a):
- Demand: $Q_d = 51 - 3P$
- Supply: $Q_s = 6P - 10$
- Set (b):
- Demand: $Q_d = 30 - 2P$
- Supply: $Q_s = -6 + 5P$
- 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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