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# MICROECONOMICS 1ST PARTIAL

question
demand
A weakly negative function of the price
question
Supply
A weakly positive function of the price
question
Equilibrium Price
The price point when Qs = Qd
question
Demand Curve
a curve showing how much of a product a consumer is willing to buy at each price point, holding all else equal
question
Demand Shifts for a Normal Good
For this kind of good, given an Income M
↑M ⇒ ↑D
so demand curve shifts right
question
Demand Shifts for an Inferior Good
For this kind of good, given an Income M
↑M⇒ ↓D
so demand curve shifts left
question
Demand Shifts for Substitutes
Given a substitute with price P,
↑Psubstitute⇒ ↑D
so demand curve shifts right
question
Demand Shifts for Complements
Given a complement with price P,
↑Pcomplement⇒ ↓D
so demand curve shifts left
question
Movements along the curve
Quantity change due to a change in the price is shown as a movement along the curve.
question
Demand Function
Quantity Demanded = D(Price, Other factors)
Mathematical relationahip where Quantity Demanded is a function of price and other factors.
question
Supply Curve
a curve showing how much of a product a seller is willing to sell at each price point, holding all else equal.
question
Supply Shifts
• Prices of inputs
• Technology
• Taxes/regulations
• Other factors
question
Supply Function
Quantity Supplied= S(Price, Other factors)
Mathematical relationship where quantity supplied is a function of price and other factors.
question
Excess Supply
⇒ sellers lower their prices
⇒ Qs decreases and Qd increases
⇒ lowering excess supply until it disappears.
question
Excess Demand
⇒ Qs increases and Qd decreases
⇒ lowering excess demand until it disappears.
question
Market Equilibrium
a situation in which quantity demanded equals quantity supplied
question
Horizontal Demand Curve
perfectly elastic demand
example: two teenagers offering to shovel driveways after it snows. One charges \$15 per driveway while the other charges \$20. All things being equal between the two teens, no one hires the boy charging \$20. If that teen then changes his price to \$10 per driveway, the boy charging \$15 loses all of his customers.
question
Vertical Demand Curve
perfectly inelastic demand
example: If the quantity demanded shows only slight change in response to a price increase, for example, demand is inelastic. This is often the case with products that are considered necessities, such as food and housing.
question
Horizontal Supply Curve
perfectly elastic supply
example: In practice, this means that any increase in quantity demanded can be met without an increase in the price of the good.
question
Vertical Supply Curve
perfectly inelastic supply
example: No matter how much a person is willing to pay, extra amounts of that good cannot be created. Land is an example of a good with a vertical supply curve.
question
Elasticity of Demand
Measures how responsive the quantity demanded is to changes in prices.
• A horizontal demand curve -> perfectly elastic.
• A vertical demand curve -> perfectly inelastic (elasticity=0).
In general, we call demand:
• elastic -> E < -1
• unit elastic E = -1
• inelastic -1 < E < 0
question
Elasticity of Supply
Measures how responsive the quantity supplied is to changes in prices.
Supply is called
• perfectly elastic if 𝐸 → ∞
• elastic if 𝐸 > 1
• unit elastic if 𝐸 = 1
• inelastic if 𝐸 < 1
• perfectly inelastic if 𝐸 = 0.
question
Total Expenditure
P x Q
(Price P, Quantity Q)
question
Change in Total Expenditure
= P ⋅ ΔQ + ΔP ⋅ Q
(Price P, Quantity Q)
question
Change in total expenditure over change in price
𝛥TE/ 𝛥P = (Ed + 1)xQ
Note: it's the derivative
question
income elasticity of demand
measures of the responsive the quantity demanded is to changes in income M.
𝐸dm = (ΔQd/Qd)/(ΔM/M)
• 𝐸dm > 0 ⇒ normal good
• 𝐸dm < 0 ⇒ inferior good
question
cross-price elasticity of demand
Measures how responsive the demand for one good is to changes in the price of another good.
𝐸dP0 = (ΔQd/Qd)/(ΔP0/P0)
• 𝐸dP0 > 0 ⇒ substitute good
• 𝐸dP0 < 0 ⇒ complement
• 𝐸dP0 = 0 ⇒ independent goods
question
Preference
It tells us about a consumer's likes and dislikes.
It determines the choices individuals make, such as
• how much an individual is willing to pay for a good
• the rate at which an individual is willing to substitute one good against another.
question
Utility Functions
Functions used to describe consumer preferences.
question
Indifference Curves
curves showing all consumption bundles that a consumer likes equally well (bunldes that give the consumer the same utility)
question
Properties of Indifference Curves
1. Higher indifference curves are preferred to lower ones
2. Indifference curves are downward sloping
3. Indifference curves do not cross
4. Indifference Curves are THIN
question
Consumption Bundle
the collection of goods that an individual consumes over a given period
question
More-is-better Assumption
when a given consumption bundle A contains more of every good than a second bundle B, a consumer prefers bdl A over bdl B.
question
Ranking Assumption
A consumer can rank in order of preference all potential available choices (ties are possible)
question
Rational Choice Assumption
Among all available options, a consumer will select the one they rank highest
question
Properties of Preference: Completeness
Between any pair of alternatives A and B a consumer either prefers A over B, B over A, or is indifferent between them.
question
Properties of Preference: Transitive
If a consumer prefers a given alternative A over B, and B over C, then the consumer will also prefer alternative A over C.
question
Plotting Indifference Curves
Suppose Utility U is given by U=CxF
1. Solve for good on vertical axis: C=U/F
2. Pick an arbitrary Utility level and plot.
question
Substitution Between Goods
A consumer can substitute goods at a rate that leaves them indifferent between bundles. (Along the IC)
question
Marginal Rate of Substitution (MRS)
The rate at which a consumer must adjust Y to maintain the same Utility level when X changes marginally:
MRSxy = -ΔY/ΔX
It is equal to the negative of the slope of the tangent to the indifference curve at point A (see example on notes for point A(3,3)
question
Utility
A numeric value representing a consumer's relative well being.
question
Utility Formula
A formula that assigns a utility value to each consumption bundle
e.g. U(F,C) = 3F + 2C + 2CF
Special Cases:
-> Perfect Substitutes X,Y:
U(X,Y) = aX + bY
->Perfect Complement X,Y:
U(X,Y) = min(aX, bY)
question
MRS in Utility Functions
(MUx)/(MUy)
question
Cobb-Douglas Utility Function
U(X,Y) = X^α * Y^β
question
Quasi-linear Utility Functions
U(X,Y) = f(X) + Y
question
MRS in Cobb-Douglas Utility Function
αY / βX
question
Utility Function for Perfect Substitutes
U(X,Y) = 𝛼X + 𝛽Y
question
Utility Function for Perfect Complements
U(X,Y) = min(𝛼X, 𝛽Y)
question
E.g. waiting time at the doctor: • Suppose utility depends on waiting time 𝑤 and quality 𝑞: 𝑈(𝑤,𝑞) = 20 − 𝑤 + 2𝑞.
• To draw an IC:
- Pick some 𝑈, say 𝑈 = 10
- Solve for variable on vertical axis, say 𝑤 = 10 + 2𝑞𝑞
⇒ upward sloping IC!
question
Budget Constraint
cost of consumption bundle ≤ income
question
Budget Line Equation
PaA x PbB = M
Where Pa,Pb are the prices of goods A and B respectively, A, B are the number of units of A and B, and M is the income.
When this equation is satifyied, we are on the budget line.
question
Properties of Budget Lines
1. Budget lines separate affordable and unaffordable consumption bundles
2. The slope of the budget line is given by −𝑃X/𝑃Y, where 𝑋 is the good on the horizontal axis.
3. The budget line cuts the horizontal axis at 𝑀/𝑃𝑋 and the vertical axis at 𝑀/𝑃Y.
4. An income change implies a parallel shift of the budget line
5. A price change rotates the budget line around the intersection with the axis of the good with the unchanged price (inward rotation for a price rise)
6. Multiplying all prices by the same number has the same effect as dividing income by that number.
question
Interior Solution
A consumption choice problem has an interior solution if there are other affordable bundles with a bit more of one and a bit less of the other good
question
Boundary Solution
An optimal consumption bundle that does not contain at least a bit of every good is called a boundary solution
question
Properties of Best Choices
1. The consumer's best choice lies on the budget line
2. At an interior solution, indifference curve and budget line are tangent, and hence MRSxy = 𝑃𝑋/PY
3. The intersection of an indifference curve and the budget line cannot be optimal at an interior solution
4. For indifference curves with declining MRS (convex preferences), an interior choice that satisfies the tangency condition always is the best affordable choice.
question
Optimal Choice
the choice which maximizes the consumer's utility function subject to the budget constraint.
question
How to Find Optimal Consumption Quantities
Solution must lie on the budget line (i.e. 𝑃𝑋 + 𝑃𝑌 = 𝑀)
Taken together, we have two conditions that determine optimal consumption quantities 𝑋 and 𝑌:
• Being on the budget line: 𝑃x𝑋 + 𝑃y𝑌 = 𝑀
• Tangency: MRSxy = 𝑃𝑋/𝑃𝑌
⇒ Given a specific utility function, we can compute MUx and MUy (and hence MRSxy), and solve for optimal quantities 𝑋 and 𝑌.
question
Optimal Consumption Quantities for Perfect Complements
If X and Y are perfect complements (utility function 𝑈(𝑋,𝑌) = min{𝛼X, 𝛽Y}), they are purchased at a constant ratio 𝑋/𝑌 = 𝛽/𝛼, irrespective of prices
• Quantities of X and Y in the optimal bundle C are found by solving the following system
𝑃x𝑋 + 𝑃y𝑌 = 𝑀
𝑋/𝑌 = 𝛽/𝛼
question
Optimal Consumption Quantities for Perfect Substitutes
If X and Y are perfect substitutes (utility function 𝑈(𝑋,𝑌) = 𝛼X + 𝛽Y, consumers spend their income
- entirely on X if MRSxy = 𝛼/𝛽 > 𝑃𝑋/𝑃𝑌
- entirely on Y if MRSxy = 𝛼/𝛽 < 𝑃𝑋/𝑃𝑌
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question
demand
A weakly negative function of the price
question
Supply
A weakly positive function of the price
question
Equilibrium Price
The price point when Qs = Qd
question
Demand Curve
a curve showing how much of a product a consumer is willing to buy at each price point, holding all else equal
question
Demand Shifts for a Normal Good
For this kind of good, given an Income M
↑M ⇒ ↑D
so demand curve shifts right
question
Demand Shifts for an Inferior Good
For this kind of good, given an Income M
↑M⇒ ↓D
so demand curve shifts left
question
Demand Shifts for Substitutes
Given a substitute with price P,
↑Psubstitute⇒ ↑D
so demand curve shifts right
question
Demand Shifts for Complements
Given a complement with price P,
↑Pcomplement⇒ ↓D
so demand curve shifts left
question
Movements along the curve
Quantity change due to a change in the price is shown as a movement along the curve.
question
Demand Function
Quantity Demanded = D(Price, Other factors)
Mathematical relationahip where Quantity Demanded is a function of price and other factors.
question
Supply Curve
a curve showing how much of a product a seller is willing to sell at each price point, holding all else equal.
question
Supply Shifts
• Prices of inputs
• Technology
• Taxes/regulations
• Other factors
question
Supply Function
Quantity Supplied= S(Price, Other factors)
Mathematical relationship where quantity supplied is a function of price and other factors.
question
Excess Supply
⇒ sellers lower their prices
⇒ Qs decreases and Qd increases
⇒ lowering excess supply until it disappears.
question
Excess Demand
⇒ Qs increases and Qd decreases
⇒ lowering excess demand until it disappears.
question
Market Equilibrium
a situation in which quantity demanded equals quantity supplied
question
Horizontal Demand Curve
perfectly elastic demand
example: two teenagers offering to shovel driveways after it snows. One charges \$15 per driveway while the other charges \$20. All things being equal between the two teens, no one hires the boy charging \$20. If that teen then changes his price to \$10 per driveway, the boy charging \$15 loses all of his customers.
question
Vertical Demand Curve
perfectly inelastic demand
example: If the quantity demanded shows only slight change in response to a price increase, for example, demand is inelastic. This is often the case with products that are considered necessities, such as food and housing.
question
Horizontal Supply Curve
perfectly elastic supply
example: In practice, this means that any increase in quantity demanded can be met without an increase in the price of the good.
question
Vertical Supply Curve
perfectly inelastic supply
example: No matter how much a person is willing to pay, extra amounts of that good cannot be created. Land is an example of a good with a vertical supply curve.
question
Elasticity of Demand
Measures how responsive the quantity demanded is to changes in prices.
• A horizontal demand curve -> perfectly elastic.
• A vertical demand curve -> perfectly inelastic (elasticity=0).
In general, we call demand:
• elastic -> E < -1
• unit elastic E = -1
• inelastic -1 < E < 0
question
Elasticity of Supply
Measures how responsive the quantity supplied is to changes in prices.
Supply is called
• perfectly elastic if 𝐸 → ∞
• elastic if 𝐸 > 1
• unit elastic if 𝐸 = 1
• inelastic if 𝐸 < 1
• perfectly inelastic if 𝐸 = 0.
question
Total Expenditure
P x Q
(Price P, Quantity Q)
question
Change in Total Expenditure
= P ⋅ ΔQ + ΔP ⋅ Q
(Price P, Quantity Q)
question
Change in total expenditure over change in price
𝛥TE/ 𝛥P = (Ed + 1)xQ
Note: it's the derivative
question
income elasticity of demand
measures of the responsive the quantity demanded is to changes in income M.
𝐸dm = (ΔQd/Qd)/(ΔM/M)
• 𝐸dm > 0 ⇒ normal good
• 𝐸dm < 0 ⇒ inferior good
question
cross-price elasticity of demand
Measures how responsive the demand for one good is to changes in the price of another good.
𝐸dP0 = (ΔQd/Qd)/(ΔP0/P0)
• 𝐸dP0 > 0 ⇒ substitute good
• 𝐸dP0 < 0 ⇒ complement
• 𝐸dP0 = 0 ⇒ independent goods
question
Preference
It tells us about a consumer's likes and dislikes.
It determines the choices individuals make, such as
• how much an individual is willing to pay for a good
• the rate at which an individual is willing to substitute one good against another.
question
Utility Functions
Functions used to describe consumer preferences.
question
Indifference Curves
curves showing all consumption bundles that a consumer likes equally well (bunldes that give the consumer the same utility)
question
Properties of Indifference Curves
1. Higher indifference curves are preferred to lower ones
2. Indifference curves are downward sloping
3. Indifference curves do not cross
4. Indifference Curves are THIN
question
Consumption Bundle
the collection of goods that an individual consumes over a given period
question
More-is-better Assumption
when a given consumption bundle A contains more of every good than a second bundle B, a consumer prefers bdl A over bdl B.
question
Ranking Assumption
A consumer can rank in order of preference all potential available choices (ties are possible)
question
Rational Choice Assumption
Among all available options, a consumer will select the one they rank highest
question
Properties of Preference: Completeness
Between any pair of alternatives A and B a consumer either prefers A over B, B over A, or is indifferent between them.
question
Properties of Preference: Transitive
If a consumer prefers a given alternative A over B, and B over C, then the consumer will also prefer alternative A over C.
question
Plotting Indifference Curves
Suppose Utility U is given by U=CxF
1. Solve for good on vertical axis: C=U/F
2. Pick an arbitrary Utility level and plot.
question
Substitution Between Goods
A consumer can substitute goods at a rate that leaves them indifferent between bundles. (Along the IC)
question
Marginal Rate of Substitution (MRS)
The rate at which a consumer must adjust Y to maintain the same Utility level when X changes marginally:
MRSxy = -ΔY/ΔX
It is equal to the negative of the slope of the tangent to the indifference curve at point A (see example on notes for point A(3,3)
question
Utility
A numeric value representing a consumer's relative well being.
question
Utility Formula
A formula that assigns a utility value to each consumption bundle
e.g. U(F,C) = 3F + 2C + 2CF
Special Cases:
-> Perfect Substitutes X,Y:
U(X,Y) = aX + bY
->Perfect Complement X,Y:
U(X,Y) = min(aX, bY)
question
MRS in Utility Functions
(MUx)/(MUy)
question
Cobb-Douglas Utility Function
U(X,Y) = X^α * Y^β
question
Quasi-linear Utility Functions
U(X,Y) = f(X) + Y
question
MRS in Cobb-Douglas Utility Function
αY / βX
question
Utility Function for Perfect Substitutes
U(X,Y) = 𝛼X + 𝛽Y
question
Utility Function for Perfect Complements
U(X,Y) = min(𝛼X, 𝛽Y)
question
E.g. waiting time at the doctor: • Suppose utility depends on waiting time 𝑤 and quality 𝑞: 𝑈(𝑤,𝑞) = 20 − 𝑤 + 2𝑞.
• To draw an IC:
- Pick some 𝑈, say 𝑈 = 10
- Solve for variable on vertical axis, say 𝑤 = 10 + 2𝑞𝑞
⇒ upward sloping IC!
question
Budget Constraint
cost of consumption bundle ≤ income
question
Budget Line Equation
PaA x PbB = M
Where Pa,Pb are the prices of goods A and B respectively, A, B are the number of units of A and B, and M is the income.
When this equation is satifyied, we are on the budget line.
question
Properties of Budget Lines
1. Budget lines separate affordable and unaffordable consumption bundles
2. The slope of the budget line is given by −𝑃X/𝑃Y, where 𝑋 is the good on the horizontal axis.
3. The budget line cuts the horizontal axis at 𝑀/𝑃𝑋 and the vertical axis at 𝑀/𝑃Y.
4. An income change implies a parallel shift of the budget line
5. A price change rotates the budget line around the intersection with the axis of the good with the unchanged price (inward rotation for a price rise)
6. Multiplying all prices by the same number has the same effect as dividing income by that number.
question
Interior Solution
A consumption choice problem has an interior solution if there are other affordable bundles with a bit more of one and a bit less of the other good
question
Boundary Solution
An optimal consumption bundle that does not contain at least a bit of every good is called a boundary solution
question
Properties of Best Choices
1. The consumer's best choice lies on the budget line
2. At an interior solution, indifference curve and budget line are tangent, and hence MRSxy = 𝑃𝑋/PY
3. The intersection of an indifference curve and the budget line cannot be optimal at an interior solution
4. For indifference curves with declining MRS (convex preferences), an interior choice that satisfies the tangency condition always is the best affordable choice.
question
Optimal Choice
the choice which maximizes the consumer's utility function subject to the budget constraint.
question
How to Find Optimal Consumption Quantities
Solution must lie on the budget line (i.e. 𝑃𝑋 + 𝑃𝑌 = 𝑀)
Taken together, we have two conditions that determine optimal consumption quantities 𝑋 and 𝑌:
• Being on the budget line: 𝑃x𝑋 + 𝑃y𝑌 = 𝑀
• Tangency: MRSxy = 𝑃𝑋/𝑃𝑌
⇒ Given a specific utility function, we can compute MUx and MUy (and hence MRSxy), and solve for optimal quantities 𝑋 and 𝑌.
question
Optimal Consumption Quantities for Perfect Complements
If X and Y are perfect complements (utility function 𝑈(𝑋,𝑌) = min{𝛼X, 𝛽Y}), they are purchased at a constant ratio 𝑋/𝑌 = 𝛽/𝛼, irrespective of prices
• Quantities of X and Y in the optimal bundle C are found by solving the following system
𝑃x𝑋 + 𝑃y𝑌 = 𝑀
𝑋/𝑌 = 𝛽/𝛼
question
Optimal Consumption Quantities for Perfect Substitutes
If X and Y are perfect substitutes (utility function 𝑈(𝑋,𝑌) = 𝛼X + 𝛽Y, consumers spend their income
- entirely on X if MRSxy = 𝛼/𝛽 > 𝑃𝑋/𝑃𝑌
- entirely on Y if MRSxy = 𝛼/𝛽 < 𝑃𝑋/𝑃𝑌

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