Micro Flashcards
Economic model
Provide simplified portraits of the way individuals make decisions, firms behave, and the way these two interact to establish markets.
Two general methods used to verify economic models
- Direct approach seeks to establish validity of the basic assumptions the model is based on. 2. Indirect approach shows that a simplified model correctly predicts real world events.
3 general features of economic models
Ceteris Paribus assumption, economic decision makers seek to optimise something, distinction between positive and normative questions
Exogenous variables
Variables that are outside of the decision makers control. E.g households: price of goods, firms: price of inputs
Endogenous variables
Variables that are determined within a model as the result of a decision. E.g household: quantities bought, firms: output produced
Agents
Rational and optimise. They choose the best given some economic constraints. Assume they have perfect information.
Supply in competitive market
Sellers bring these to the market. The goods could be exchanged for other goods or income. If selling goods doesn’t make an improvement, rationality will prevent suppliers from producing.
Demand in competitive market
Buyers of goods have a reservation price, maximum willingness to pay.
Perfect competition
Buyers and sellers have no influence on price or quantity so R = p*q
Equilibrium in competitive market
Prices adjust until demand equals supply. The market clears
Ordinary monopoly
Seller can influence price by controlling supply, R = p(q)*q
Positive economics
Descriptive. Determines how resources are in fact allocated in an economy.
Normative economics
Judgemental. Taking a stance about what should be done.
Pareto improvement
Occurs if one persons welfare can be improved without detriments to others. If not possible, we have Pareto efficiency
Although marshallian model is useful …
It is a partial equilibrium model, looking at only one market at a time.
Production possibility frontier
Various amounts of two goods that an economy can produce using its available resources during some period. Reminds us that resources are scarce. Shows us the opportunity cost of producing more of one good as the decrease in amount of the other.
Preference
Is a binary relation over objects of choice
Satiation
The effect where the more of a good one possesses, the less one is willing to give up to get more of it. Once you pass satiation point, consuming more means enjoying it less.
Utility
A function that represents a preference.
Utility function
Translates the behaviour of the consumer into a mathematical function.
Utility rankings
Ordinal rankings. It’s not possible to compare utilities of different people.
Preferences must be..
Rational: complete and transitive and monotone
A preference is complete if:
x>y or y>x or both (x~y)
A preference relation is transitive if:
x>y and y>z then x>z
A preference relation is continuous if:
The upper contour and low contour sets are closed. The sets have no holes.
Consequence of transitivity
Different indifference curves cannot intersect
Ordinal utility
Any increasing transformation of a utility function also gives a utility function
Ordinal
Tells us that one bundle is better than another. Doesn’t tells by how much.
Indifference curve
Represents all alternative combinations of x and y for which an individual is equally well off.
why is the slope of an IC negative
to show that if the individual is forced to give up some of y, they must be compensated by an additional amount of x to remain indifferent between two bundles.
convexity definition
a set of points is said to be convex if any two points within the set can be joined by a straight line that is contained completely within the set. Implies that ICs are differentiable almost everywhere.
strict convexity
assume differentiability everywhere,
marginal rate of substitution
is the negative tradeoff between two goods - (dU/dx)/(dU/dy), px/py
perfect substitutes: U(x) = ax1 + bx2
MRS is constant (equal to a/b), convexity holds.
perfect complements: U(x) = min{ax1, bx1}
smallest numbers decide utility, MRS = 0/infinity/not defined. strict not strong monotonicity. convexity but not strict convexity. L-shaped ICs. consumption occurts at the vertices of the ICs.
Cobb Douglas: U(x) = x^a + x^b
satisfy all requirements in strongest form: convexity and monotonicity. MRS changes along Ic.
constant elasticity of substition: U(x) = (x^§ + x^§)^1/§
value of delta is not euqal to 0 but smaller than 1. if delta was larger than 1, IC would be concave. when delta = 1, this is perfect subtitutes. as delta approaches 0, the function approaches Cobb Douglas. as delta approaches negative infinity, the function approaches perfect complements.
Shephards Lemma
dE/dpi = h*i
Marshallian demand solves
maximisation problem
Hicksean demand solves
minimisation problem
Roy’s identity
x*i = - Vpi / Vy. Consumers demand given by ratio of marginal indirect utilities.
corner solution
an individual’s preferences may be such that they obtain maximum utility by choosing no amount of one of the goods.
marshallian demand for cobb douglas
x1=(ay)/p1, x2=(by)/p2
direct utility
utility across all possible consumption bundles
indirect utility
represents the maximum utility a consumer can attain given the prices of goods and the consumer’s income. Substituting marshallian demand into utility function gives indirect utility. V(p,w) = max U(x) subject to p*x <= w
properties of indirect utility
continuous in prices, utility and income, small changes have small effects. assume differentiability. homogenous of degree 0, strictly increasing in income and decreasing in prices.
properties of the expenditure function
continuous in prices and target utility. homogenous of degree 1 in prices. expenditure function and indirect utility are inverse functions of one another. expenditure is strictly increasing and unbounded in target utility. non-decreasing and concave in prices
homogenous of degree 0
if you change prices and income, the outcome doesnt change
homogenous of degree 1
if you double prices, outcome doubles
normal good
dx/dm >= 0
inferior good
dx/dm < 0
income effect
the change in demand for a good caused by a change in consumer’s purchasing power or real income.
substitution effect
consumers replace one good with another due to price change
increase in demand
outward shift of demand curve
increase in quantity demanded
movement along the curve
compensated demand function can be found from
differentiating expenditure function with respect to prices
inferior good def
when income increases, consumption decreases
income elasiticty def
measures the sensitivity of changes in consumption relative to changes in income.
income elasticity formula
(dxi/dm)(m/xi)
own price elasiticty
changes in demand relative to changes in price: (dxi/dpi)(pi/xi)
cross price elasiticty
(dxi/dpj)(pj/xi)
inelastic demand
-1 < e < 0
elastic demand
e < -1
slutsky equation in elasticity form
e = ẽ - se, where s=(px/m) is income share
whether hicksean and marshallian price elasticities differ much depends on…
the importance of income effects in the overall demand.
the slutsky elasticity equation shows that hicksean and marshallian own-price elasticities will be similar if….
either of the two conditions hold: 1) the share of income devotes to x is small, 2) the income elasticity of demand of x is small. These both reduce the importance of the income effect
engel’s law
percentage of income allocated for food purchases decreases as a household’s income rises, while the percentage spent on other things increases.
cournot aggregation
budget share s1 of good 1 is small when good 1 has many substitutes (ϵi1>0), and big when it has many complements (ϵi1<0)
euler theorem
the net sum of all price elasticities together with the income elasticity for a good must sum to zero
consumer surplus
monetary measure of the utility gains and losses that individuals experience when price changes. Area below the compensated demand curve and above market price.
compensating variation
compensation required to reach same utility level after a price change: CV = E(p1x, py, U) - E(p0x, py, U)