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Questions and Answers
What does a function assign to each incoming number?
What does a function assign to each incoming number?
In the context of a function, which variable is considered dependent?
In the context of a function, which variable is considered dependent?
If quantity demanded, Q, depends on market price, P, how can this relationship be expressed?
If quantity demanded, Q, depends on market price, P, how can this relationship be expressed?
What characterizes inverse functions f and g?
What characterizes inverse functions f and g?
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When analyzing the demand function P = -2Q + 50, what does P equal when Q is 0?
When analyzing the demand function P = -2Q + 50, what does P equal when Q is 0?
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What can be inferred about the slope of a typical demand function?
What can be inferred about the slope of a typical demand function?
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What do the parameters a and b represent in the linear demand function hypothesis P = aQ + b?
What do the parameters a and b represent in the linear demand function hypothesis P = aQ + b?
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Which statement correctly distinguishes a model from an equation?
Which statement correctly distinguishes a model from an equation?
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What type of function describes the relationship where P is a decreasing function of Q?
What type of function describes the relationship where P is a decreasing function of Q?
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In the equation P = -3Q + 75, which variable is dependent?
In the equation P = -3Q + 75, which variable is dependent?
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From the supply function P = aQ + b with a > 0, what happens to P as Q increases?
From the supply function P = aQ + b with a > 0, what happens to P as Q increases?
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If the demand function is P = -2QD + 50, what does the slope indicate about QD?
If the demand function is P = -2QD + 50, what does the slope indicate about QD?
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Which of the following best describes the concept of endogenous variables?
Which of the following best describes the concept of endogenous variables?
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What is the dependent variable in the demand function P = -2QD + 50?
What is the dependent variable in the demand function P = -2QD + 50?
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Which of the following represents the equilibrium quantity when the demand function is P = -4QD + 20 and the supply function is P = 2QS + 2?
Which of the following represents the equilibrium quantity when the demand function is P = -4QD + 20 and the supply function is P = 2QS + 2?
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How does a fixed tax of £5 on each good affect the supply function P = 0.5QS + 25?
How does a fixed tax of £5 on each good affect the supply function P = 0.5QS + 25?
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If the new supply function, after imposing a £5 tax, is represented as P = 0.5QS + 30, what will be the effect on the equilibrium price?
If the new supply function, after imposing a £5 tax, is represented as P = 0.5QS + 30, what will be the effect on the equilibrium price?
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In the context of the equation P = -2QD + 50, what does the coefficient -2 represent?
In the context of the equation P = -2QD + 50, what does the coefficient -2 represent?
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Which equation would likely represent demand if P = -3QD + 15?
Which equation would likely represent demand if P = -3QD + 15?
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What is the point of intersection for the functions P = -2QD + 50 and P = 0.5QS + 25?
What is the point of intersection for the functions P = -2QD + 50 and P = 0.5QS + 25?
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What is the significance of solving both demand and supply equations simultaneously?
What is the significance of solving both demand and supply equations simultaneously?
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Study Notes
Supply & Demand Analysis
- Supply & demand analysis examines the relationship between supply and demand for goods and services.
- A function assigns a unique output (y) for a given input (x).
- Functions can be expressed as y = 2x + 3 or f(x) = 2x + 3.
- Independent variables are inputs, while dependent variables are outputs.
Independent and Dependent Variables
- Incoming variable is the independent variable, while outgoing is the dependent variable.
- The value of the dependent variable relies on the independent variable.
- Example: In microeconomics, the quantity demanded of a product depends on its price; This can be expressed as Q = f(P).
Linear Functions
- A function is hypothesized to be linear.
- This means: P = aQ + b, where a and b are parameters.
Models and Equations
- Models use economic laws to explain and forecast real-world situations.
- Complex models often involve complicated mathematics.
- Models are more accurate representations than simpler equations.
Linear Demand Function
- A typical linear demand function is: P = -2Q + 50.
- To graph a linear demand function, find P when Q = 0 and Q when P = 0.
- P = 50 when Q = 0.
- Q = 25 when P = 0.
Graph of Typical Linear Demand Function
- The demand curve slopes downward as price increases.
- The slope of this line is negative (a < 0).
- The intercept (b) is positive (b > 0).
Elementary Theory
- Demand generally decreases as prices increase.
- Thus, the slope of a demand curve is negative.
- Price is a decreasing function of Q (quantity)
Task
- Determine if the given function (P = -3Q + 75) is a demand or supply curve.
- Identify where the curve intersects the x and y axes.
- Calculate P when Q = 23 and Q when P = 18
Model Simplification
- Models are often simplified representations of complex reality.
- Factors like income, prices of related goods, and tastes are essential but excluded in initial models.
- Q = f (P,Y,PS,PC,T)
Equilibrium
- Equilibrium occurs when quantity supplied equals quantity demanded.
Example Calculation of Equilibrium Price and Quantity
- Given demand and supply functions (P = -2QD + 50; P = 0.5Qs + 25)
- Equate both expressions to find Q.
- Q = 10.
- Substitute Q in either equation to find P (P=30.
Equilibrium Price and Quantity (Another Example)
- Given demand and supply functions (P = -4QD + 20; P = 2Qs + 2)
- Equate both expressions to find Q.
- Q = 3
- Substitute Q in either equation to find P (P=8).
Tax Impact on Market Equilibrium
- Introducing a fixed tax on each good affects the supply curve.
- The new supply curve shifts upward by the amount of the tax.
- Example: If the tax is £5, then the new supply equation becomes P = 0.5Q + 30.
Additional Tax Problem
- Identifying the demand and supply curve in P = 3Q + 24; P = -Q + 160.
- The supply curve has a tax of £16.
- Find the equilibrium price and quantity.
Two-Commodity Model
- Analyze the equilibrium prices and quantities for a two-commodity model and solve simultaneous equations.
- Determining Equilibrium price and quantities for a two commodity model by substituting for the simultaneous linear equations.
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Description
This quiz covers the fundamental concepts of supply and demand analysis, including the roles of independent and dependent variables. It explores linear functions and the use of models and equations in economics. Test your understanding of how these elements interact within economic frameworks.
