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Micro-economics summary Vu EBE
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summary of the subject of micro-economics, given in the first year of the study of economics and business economics at the Vu of Amsterdam.
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Micro economics summaryWeek 1
Preferences
- An economic model is a simplified representation of real life.
- Trade-off between applicability and manageability.
Who use economic models?
Central Planning Bureau = CPB
Central Banks = ECB and DNB
Ministries, etc.
Market equilibrium: Demand equals supply.
Supply depends on:
Production technology
Costs of inputs
Market price
Demand depends on:
Preferences of consumers
Income of consumers
Market price
Prices of other goods
Consumers buy bundle of goods.
Allocating scarce resources: size of the bundle is limited by the budget.
Budget is used to:
Buy consumer goods.
Save (intertemporal decision making).
Enjoy leisure (labor supply decision).
Consumers make choice for bundle of goods based on rationality.
Maximize utility (which is well-being or happiness).
Preference (or taste) decides ‘amount of’ happiness (utility) a consumer derives from a bundle of
goods. Preferences differ between consumers.
Assumptions:
1. Completeness: Consider a bundle A and a bundle B, then the consumer either has a
preference for bundle A, a preference for bundle B, or is indifferent.
2. Transitivity: If a consumer prefers bundle A over bundle B and bundle B over bundle C, then
the consumer prefers bundle A over bundle C.
3. More is better: If bundle A contains for all goods at least the same amount as bundle B and
for at least one good more, then a consumer prefers bundle A over bundle B.
A consumer who has the same preference for two bundles, is indifferent between these bundles.
Indifference curve: collection of all bundles of goods for which the consumer is indifferent.
Economists use utility to describe the valuation of a bundle to a consumer. All bundles on a
indifference curve have the same utility.
,Properties of indifference curves:
- Non-increasing.
- Never cross.
- Further away from the origin implies a higher utility.
- Each bundle belongs to an indifference curve.
Indifference curve is downward sloping. So reducing the amount of good X can (often) be
compensated by increasing the amount of good Y (without affecting utility).
Marginal rate of substitution: extent to which goods can be traded against each other without
affecting utility.
MRS = marginal rate of substitution.
MRS = the derivative of the indifference curve.
qy difference in the amount of good Y in bundle and qx difference in the amount of good X in
bundle.
Budget and optimization
Consumers have preferences for bundles of goods.
Preferences of consumers satisfy 3 assumptions:
1. Completeness.
2. Transitivity.
3. More is better.
The extent to which the consumer likes a bundle is called utility by economists. Indifference curves
show all bundles of goods with the same utility. The marginal rate of substitution shows how two
goods in a bundle can be traded without affecting the utility of the bundle.
Preferences are summarized in a utility function. A utility function gives a numerical value to a bundle
of goods (amount of utility). Utility is an ordinal measure. Magnitude of utility is not relevant, only
the (relative) ranking of bundles is important.
The utility function U(qx,qy) describes how much utility the consumer receives from having this
bundle of goods.
If a consumer prefers a bundle (qx,qy) over a bundle (q’x,q’y) then U(qx,qy) > U(q’x,q’y).
If a consumer is indifferent between the bundles then U(qx,qy) = U(q’x,q’y).
Indifference curves: All bundles (qx,qy) for which U(qx,qy) = Ū.
A utility function must satisfy the assumptions on preferences.
Completeness: Utility functions assigns a value to each bundle of goods.
Transitivity: If U > U’ and U’ > U’’ then U > U’’.
More is better: If qx q’x and qy q’y then U U’.
Marginal utility describes how much utility increases if the amount of a good in the bundle increases
with one.
More is better implies that marginal utility cannot be negative!!!
Marginal utility (of good X):
, implies that the amount of good Y remains constant.
How many additional units of good Y are required to replace one unit of good X.
qy is the change in the amount of good Y.
Changing the bundle while keeping the utility constant.
Then the marginal rate of substitution follows:
When MRS is small, only a few additional units of good Y are
necessary to replace one unit of good X.
Limited budget: a constraint on the amount of consumption.
Opportunity set: all bundles (qx,qy) that can be bought with
the budget.
Marginal rate of transformation: How much the consumer
should sell of good Y to be able to buy one additional unit of good X within the same budget.
MRT determines the slope (or gradient) of the budget line.
MRT does not change if the budget increases (then only the opportunity set expands).
MRT changes if the price of one good changes.
Consumers want to have the highest possible utility given their available budget.
So, max U(qx,qy) qx ,qy
But the bundle most lie within the opportunity set. So, utility maximization with restrictions:
pxqx + pyqy ≤ B qx ≥ 0 qy ≥ 0
Consumers cannot buy negative amounts of a good.
The bundle of goods is optimal if:
1. The bundle lies on the budget line.
2. The marginal rate of substitution equals the marginal rate of transformation
MRT = MRS (and it does not matter how you spend an additional euro.
Corner solution when indifference curves are relatively ‘flat’. But also in case of non-convex
indifference curves.
Concave indifference curves always give corner solutions. But such indifference curves are unlikely.
Consumer has a strong preference for only a homogenous bundle of goods instead of a differentiated
bundle.
Determining the optimal bundle:
1. Determine bundle with MRS = MRT.
2. Compare utility in corner solutions with utility when MRS = MRT.
The utility function describes how much a consumer valuates each bundle.
The budget determines the opportunity set.
Optimal bundle is the bundle in the opportunity set which yields the highest utility.
Because more is better the optimal bundle always lies on the budget line.
For the interior solution holds MRS = MRT.
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