ECON 410 Chapter 1

Constrained Optimization:

used when a decision maker seeks to make the best (optimal) choice, considering any possible limitations or restrictions on the choices.

Almost all microeconomic models rely on just 3 key analytical tools

1. Constrained optimization 2. Equilibrium analysis 3. Comparative statics

Endogenous variable:

a variable whose value is determined within the model being studied

Positive analysis

analysis that attempts to explain how an economic system works or to predict how it will change over time. Asks explanatory questions, "What has happened?" or "What is happening?" and predictive questions "What will happen if some exogenous variable changes?"

Normative analysis

analysis that typically focuses on issues of social welfare, examining what will enhance or detract from the common good. Asks prescriptive questions, "What should be done?"

Comparative Statics

analysis used to examine how a change in some exogenous variable will affect the level of some endogenous variable in an economic system

Constrained Optimization Example

farmer with F feet in fence wanting to maximize area with L and W. Max (objective function): LW Endogenous variables (L, W) subject to (constraints): 2L + 2W <= F

Positive questions examples

farmer's fencing problem. "What dimensions of the sheep's pen will the farmer choose to maximize the area of the pen?"

Constraints

in a constrained optimization problem, constraints represent restrictions or limits that are imposed on the decision maker

Equilibrium

in a system, equilibrium is a state or condition that will continue indefinitely if exogenous factors remain unchanged.

Economics

is the science that deals with the allocation of limited resources to satisfy unlimited human wants i.e. the science of constrained choice - What goods and services will be produced, and in what quantities? - Who will produce the goods and services, and how? - Who will receive the goods and services?

Exogenous variable

one whose value is taken as given in the model

Objective function

relationship that the decision maker seeks to "optimize"

This allows us to do a "before-and-after" analysis by comparing two snapshots of an economic model

1st snapshot tells us the levels of the endogenous variable given a set of initial values of exogenous variables 2nd snapshot tells us how an endogenous variable we care about has changed in response to an exogenous shock- a change in the level of some exogenous variable. Ex: Iran produces pistachios. $1 billion in 2007. Drought and cold weather in 2008 leads to 1/3 production. Exogenous shock results in price rising by 26%.

Economists construct and analyze economic models, or formal descriptions, of the problems they are addressing. Like how a roadmap is the essentials of a complex terrain (roads, houses, stores, lots, alleys, to major streets, etc.)

All models must specify what variables will be taken as given in the analysis and what variables are to be determined.

The solution to any constrained optimization problem depends on the marginal impact of the decision variables on the value of the objective function.

Marginal cost measure the incremental impact of the last unit of the independent variable (output) on the dependent variable (total cost). $5 to increase production by one unit ($5 is the marginal cost).