Market Model Analysis Quiz

Questions and Answers

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?

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?

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 $(b + d) = 0$?

<p>They do not intersect, indicating no equilibrium.</p> Signup and view all the answers

Which equation relates demand and supply in a market model?

<p>$Q_d = Q_s$.</p> Signup and view all the answers

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.

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.