Micro and Game Theory - Custom Scholars
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# Micro and Game Theory

question
Uncompensated Demand
Maximizing utility given prices and total income
Max U(x,y) s.t. pxX + pyY = I
question
Compensated demand
Minimize expenditure while holding utility constant, given existing prices
Min PxX + PyY s.t. U(x,y) = fixed U
question
Three properties of utility functions
1. Completeness
2. Reflexivity
3. Transitivity
question
Completness
We always know the consumer's preferences between bundles. either x > y, y > x, or they are equal.
question
Reflexitivity
Each bundle is at least as good as itself
question
Transitivity
If a > b, and b > c, then a > c
question
Weak Monotonicity
If x is at least as large as bundle y, then a rational consumer will see bundle x as at least as good as bundle y. In other words, if you manually go through the bundle or vector and bundle x has at least as much of each good as bundle y, then weak monotonicity holds.
question
Strong monotonicity
Same as weak monotonicity, but if x >= y, and x and y are not the same point, then x is strongly preferred to y.
question
monotonic transformation of a utility function
a utility function that represents the same preferences as the original utility function. In a strictly increasing function, doing something like squaring or adding three to a utility function will not impact its demonstration of preferences.
question
Convexity of a utility function
If x is >= z and y >= z, then any convex combination of x and y will be preferred to bundle z. Example, 30% of x and 70% of y will still always be greater than z
question
Strict convexity
If x >= z, y >= z, and x and y are not the same, then any combination of x and y will be strictly preferred over z
question
Homogeneous function
If you can pull out a scaler and be left with the same original function, it is homogeneous
question
Homothetic preferences
The MRS of a homogeneous function does not change as a result of a monotonic transformation
question
Strictly, directly revealed preferences
When we are given prices, income, and a consumption decision at any given time, we can calculate to see if alternate bundles were feasible and thus if we would prefer them or not.
That is, if we could've afforded an alternative bundle but still decided to go with the original one, then it is strictly directly revealed preferred over the others.
question
Indirectly revealed preferences
When given two different budget sets, the bundle selected over the bundle present in both budget sets is indirectly revealed as preferred to the bundle that was not selected over the common bundle
question
Generalized Axiom of Revealed Preference (GARP)
In a chain of bundles where each bundle is preferred to the previous, the final bundle should not be strictly preferred to the first
question
Afriat's Theorem
GARP is a sufficient and necessary condition for consumption data to be consistent with utility maximization. If GARP is violated (two bundles are revealed preferred over each other) then we cannot generate a utility function that rationalizes the data.
question
Substitution effect
Describes how consumption is impacted by changing relative income, prices. when consumers react to an increase in a good's price by consuming less of that good and more of other goods
question
Income effect
expresses the impact of increased purchasing power on consumption
question
Slutsky Equation
formula for decomposing the effects of a price change into substitution and income effects. Total effect = substitution effect + income effect
question
Walrasian equilibrium
a vector of prices, and a consumption bundle for each agent, such that (i) every agent's consumption maximizes her utility given prices, and (ii) markets clear: the total demand for each commodity just equals the aggregate endowment. The excess demand function equals zero.
question
Edgeworth Box
diagram showing all possible allocations of either two goods between two people or of two inputs between two production processes
question
Finding an equilibrium price in an Edgeworth Box
1. Find a price where each party is buying and selling goods at a rate that satisfies them and where the excess demand is equal to zero.
2. Find the price vector and relative price slope that allows the MRS of the two individuals to be equal and for the excess demand to be zero
question
A Walrasian equilibrium without room for a pareto improvement yields
MRS of each party is equal to the relative price slope
question
Pareto Efficiency
describes an allocation in which the only way to make any individual or group of individuals better off would require making at least one other person worse off
question
First Welfare Theorem of Economics
the allocation of resources in a perfectly competitive equilibrium is pareto efficient. This says that a Walrasian equilibrium is pareto efficient. Allowing the markets to achieve equilibrium is hypothetically enough. However this doesn't hold in the real world because we do not have perfect property rights over all goods that influence our utility
question
When is the first welfare theorem violated?
by the existence of externalities, monopolies, any situation where market power exists
question
Walras' Law
The invisible hand will settle prices so that excess supply in one market will balance out with the excess demand in another market. For any price vector, excess demand will equal zero because if markets clear in all other settings, then the final market must clear as well.
A law stating that in a general equilibrium model, one of the market clearing constraints is redundant
and will hold if all other constraints hold.
question
Externalities in Edgeworth Boxes
Negative utility functions related to other individual's consumption of a good. If this is ignored, it can create a pareto inefficient allocation. With externalities, corner pareto efficient allocations may exist where the MRS of both agents are not equal but, because no other point on the indifference curves hold a better outcome, it is still Pareto efficient
question
constant returns to scale
the property whereby long-run average total cost stays the same as the quantity of output changes
question
increasing returns to scale
when long-run average total cost declines as output increases
question
decreasing returns to scale
when long-run average total cost increases as output increases
question
local returns to scale
Production functions that don't satisfy any of the global return to scale definitions. Instead, the output depends on where we fall in terms of capital and labor
question
producer's problem: maximizing output
set the MRTS for k and l = relative price level
question
Producer's dual problem: minimizing cost
Choosing a level of output and finding a cost function (the lowest possible amount of money spent to achieve this output)
Then take the derivative of the cost function to find marginal cost
question
Short-Run Firm Supply Curve
No entry or exit of firms. Locate the profit-maximizing quantity where price = marginal cost
question
Long-run firm supply
Pick the point where MC = ATC.
If ATC > MC, firms are losing money, some exit
If ATC < MC, firms are profiting, some join
question
Long-run industry supply
Under the assumption that individual firms' average cost function does not change, the industry supply curve is flat. // a curve that shows the relationship between price and quantity supplied by the industry once firms adjust fully to any change in market demand.
But, if more firms entering the market changes individual cost functions by making labor and capital more expensive, then the long-run industry supply curve can change over time
question
Consumer surplus
The area above the equilibrium price. Total surplus can be calculated as the sum of the difference between each individual's reservation price for the purchase and the amount they actually pay // the amount a buyer is willing to pay for a good minus the amount the buyer actually pays for it
question
Producer surplus
The inverse of consumer surplus. How much each producer made between the production requirement to the equilibrium price. // the amount a seller is paid for a good minus the seller's cost of providing it
question
Producer surplus in long-run
the existence of a producer surplus in the long-run represents some kind of rent increase throughout the economy. Whoever owns the inputs of that good is earning more
question
nominal income
question
Exchange rate method
Calculate nominal income by multiplying consumption by prices then deflating the income with the exchange rate as a fraction.
Can be problematic as it can imply that a certain country consumes more when this is actually not the case
question
Big Mac Index
Tool for calculating purchasing power parity that compares prices of a Big Mac throughout the world. Done by calculating nominal income then dividing it by the local price of the big mac.
question
Geary-Khamis method
Summation of price of good J in country K, multiplied by country K's share of the total global consumption of good K, multiplied by a currency conversion factor for country K
question
Requirements of a good approach for comparing wealth of nations
1. weak continuity
2. Dependence on prices
3. Weak ranking restriction
4. Independence of irrelevant countries
question
Weak continuity
small changes shouldn't flip the rankings
question
Dependence on prices
system cannot rank all entities the same way, it must consider prices
question
Weak ranking restriction
if one country consumes more of every good than another, our function should assign a higher number to the higher consumption country
question
Independence of irrelevant countries
a change in Pakistan shouldn't affect the ordering of France and Germany
question
Nash Equilibrium
a situation in which economic actors interacting with one another each choose their best strategy given the strategies that all the other actors have chosen
question
Iterative elimination of dominated strategies
...
question
Pure Strategy Nash Equilibrium
Nash equilibrium in which all players choose a fixed strategy
question
Mixed Strategy Nash Equilibrium
a profile of mixed strategies such that no actor could do better by switching strategies, given the other player's strategy
question
Best Response (Game Theory)
the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given
question
Subgame Perfect Nash Equilibrium
In sequential games, a sequence of decisions made by the various players such that no player has an incentive to deviate.
question
Cournot competition
A type of market competition in which the firms simultaneously and independently choose how much to produce and the market price is set so that the quantity demanded of each firm's product equals the quantity produced
1 of 57
question
Uncompensated Demand
Maximizing utility given prices and total income
Max U(x,y) s.t. pxX + pyY = I
question
Compensated demand
Minimize expenditure while holding utility constant, given existing prices
Min PxX + PyY s.t. U(x,y) = fixed U
question
Three properties of utility functions
1. Completeness
2. Reflexivity
3. Transitivity
question
Completness
We always know the consumer's preferences between bundles. either x > y, y > x, or they are equal.
question
Reflexitivity
Each bundle is at least as good as itself
question
Transitivity
If a > b, and b > c, then a > c
question
Weak Monotonicity
If x is at least as large as bundle y, then a rational consumer will see bundle x as at least as good as bundle y. In other words, if you manually go through the bundle or vector and bundle x has at least as much of each good as bundle y, then weak monotonicity holds.
question
Strong monotonicity
Same as weak monotonicity, but if x >= y, and x and y are not the same point, then x is strongly preferred to y.
question
monotonic transformation of a utility function
a utility function that represents the same preferences as the original utility function. In a strictly increasing function, doing something like squaring or adding three to a utility function will not impact its demonstration of preferences.
question
Convexity of a utility function
If x is >= z and y >= z, then any convex combination of x and y will be preferred to bundle z. Example, 30% of x and 70% of y will still always be greater than z
question
Strict convexity
If x >= z, y >= z, and x and y are not the same, then any combination of x and y will be strictly preferred over z
question
Homogeneous function
If you can pull out a scaler and be left with the same original function, it is homogeneous
question
Homothetic preferences
The MRS of a homogeneous function does not change as a result of a monotonic transformation
question
Strictly, directly revealed preferences
When we are given prices, income, and a consumption decision at any given time, we can calculate to see if alternate bundles were feasible and thus if we would prefer them or not.
That is, if we could've afforded an alternative bundle but still decided to go with the original one, then it is strictly directly revealed preferred over the others.
question
Indirectly revealed preferences
When given two different budget sets, the bundle selected over the bundle present in both budget sets is indirectly revealed as preferred to the bundle that was not selected over the common bundle
question
Generalized Axiom of Revealed Preference (GARP)
In a chain of bundles where each bundle is preferred to the previous, the final bundle should not be strictly preferred to the first
question
Afriat's Theorem
GARP is a sufficient and necessary condition for consumption data to be consistent with utility maximization. If GARP is violated (two bundles are revealed preferred over each other) then we cannot generate a utility function that rationalizes the data.
question
Substitution effect
Describes how consumption is impacted by changing relative income, prices. when consumers react to an increase in a good's price by consuming less of that good and more of other goods
question
Income effect
expresses the impact of increased purchasing power on consumption
question
Slutsky Equation
formula for decomposing the effects of a price change into substitution and income effects. Total effect = substitution effect + income effect
question
Walrasian equilibrium
a vector of prices, and a consumption bundle for each agent, such that (i) every agent's consumption maximizes her utility given prices, and (ii) markets clear: the total demand for each commodity just equals the aggregate endowment. The excess demand function equals zero.
question
Edgeworth Box
diagram showing all possible allocations of either two goods between two people or of two inputs between two production processes
question
Finding an equilibrium price in an Edgeworth Box
1. Find a price where each party is buying and selling goods at a rate that satisfies them and where the excess demand is equal to zero.
2. Find the price vector and relative price slope that allows the MRS of the two individuals to be equal and for the excess demand to be zero
question
A Walrasian equilibrium without room for a pareto improvement yields
MRS of each party is equal to the relative price slope
question
Pareto Efficiency
describes an allocation in which the only way to make any individual or group of individuals better off would require making at least one other person worse off
question
First Welfare Theorem of Economics
the allocation of resources in a perfectly competitive equilibrium is pareto efficient. This says that a Walrasian equilibrium is pareto efficient. Allowing the markets to achieve equilibrium is hypothetically enough. However this doesn't hold in the real world because we do not have perfect property rights over all goods that influence our utility
question
When is the first welfare theorem violated?
by the existence of externalities, monopolies, any situation where market power exists
question
Walras' Law
The invisible hand will settle prices so that excess supply in one market will balance out with the excess demand in another market. For any price vector, excess demand will equal zero because if markets clear in all other settings, then the final market must clear as well.
A law stating that in a general equilibrium model, one of the market clearing constraints is redundant
and will hold if all other constraints hold.
question
Externalities in Edgeworth Boxes
Negative utility functions related to other individual's consumption of a good. If this is ignored, it can create a pareto inefficient allocation. With externalities, corner pareto efficient allocations may exist where the MRS of both agents are not equal but, because no other point on the indifference curves hold a better outcome, it is still Pareto efficient
question
constant returns to scale
the property whereby long-run average total cost stays the same as the quantity of output changes
question
increasing returns to scale
when long-run average total cost declines as output increases
question
decreasing returns to scale
when long-run average total cost increases as output increases
question
local returns to scale
Production functions that don't satisfy any of the global return to scale definitions. Instead, the output depends on where we fall in terms of capital and labor
question
producer's problem: maximizing output
set the MRTS for k and l = relative price level
question
Producer's dual problem: minimizing cost
Choosing a level of output and finding a cost function (the lowest possible amount of money spent to achieve this output)
Then take the derivative of the cost function to find marginal cost
question
Short-Run Firm Supply Curve
No entry or exit of firms. Locate the profit-maximizing quantity where price = marginal cost
question
Long-run firm supply
Pick the point where MC = ATC.
If ATC > MC, firms are losing money, some exit
If ATC < MC, firms are profiting, some join
question
Long-run industry supply
Under the assumption that individual firms' average cost function does not change, the industry supply curve is flat. // a curve that shows the relationship between price and quantity supplied by the industry once firms adjust fully to any change in market demand.
But, if more firms entering the market changes individual cost functions by making labor and capital more expensive, then the long-run industry supply curve can change over time
question
Consumer surplus
The area above the equilibrium price. Total surplus can be calculated as the sum of the difference between each individual's reservation price for the purchase and the amount they actually pay // the amount a buyer is willing to pay for a good minus the amount the buyer actually pays for it
question
Producer surplus
The inverse of consumer surplus. How much each producer made between the production requirement to the equilibrium price. // the amount a seller is paid for a good minus the seller's cost of providing it
question
Producer surplus in long-run
the existence of a producer surplus in the long-run represents some kind of rent increase throughout the economy. Whoever owns the inputs of that good is earning more
question
nominal income
question
Exchange rate method
Calculate nominal income by multiplying consumption by prices then deflating the income with the exchange rate as a fraction.
Can be problematic as it can imply that a certain country consumes more when this is actually not the case
question
Big Mac Index
Tool for calculating purchasing power parity that compares prices of a Big Mac throughout the world. Done by calculating nominal income then dividing it by the local price of the big mac.
question
Geary-Khamis method
Summation of price of good J in country K, multiplied by country K's share of the total global consumption of good K, multiplied by a currency conversion factor for country K
question
Requirements of a good approach for comparing wealth of nations
1. weak continuity
2. Dependence on prices
3. Weak ranking restriction
4. Independence of irrelevant countries
question
Weak continuity
small changes shouldn't flip the rankings
question
Dependence on prices
system cannot rank all entities the same way, it must consider prices
question
Weak ranking restriction
if one country consumes more of every good than another, our function should assign a higher number to the higher consumption country
question
Independence of irrelevant countries
a change in Pakistan shouldn't affect the ordering of France and Germany
question
Nash Equilibrium
a situation in which economic actors interacting with one another each choose their best strategy given the strategies that all the other actors have chosen
question
Iterative elimination of dominated strategies
...
question
Pure Strategy Nash Equilibrium
Nash equilibrium in which all players choose a fixed strategy
question
Mixed Strategy Nash Equilibrium
a profile of mixed strategies such that no actor could do better by switching strategies, given the other player's strategy
question
Best Response (Game Theory)
the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given
question
Subgame Perfect Nash Equilibrium
In sequential games, a sequence of decisions made by the various players such that no player has an incentive to deviate.
question
Cournot competition
A type of market competition in which the firms simultaneously and independently choose how much to produce and the market price is set so that the quantity demanded of each firm's product equals the quantity produced

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