Class One Q1

Question 1

What is meant by an objective function?

Answer 1

It is the function we are to optimize

Question 2

What is meant by a choice variable?

Answer 2

It is a variable whose value the optimiser is allowed to choose (listed under instruction max/min)

Question 3

What is meant by a parameter?

Answer 3

A variable whose value we don’t know, but which we treat as a fixed number - all variables in a problem are either choice variables OR parameters

Question 4

What is meant by the feasible set of an optimisation problem?

Answer 4

The feasible set is the set of values that the choice variables are allowed to take

Question 5

What is meant by R?

Answer 5

Set of all real numbers

Question 6

What is meant by domain and codomain of a function?

Answer 6

Domain = set of objects that can be taken as inputs into a function
Codomain = set of objects that can be outputted by the function

Question 7

What is meant by the range of a function?

Answer 7

Subset of the codomain

Eg. For f(x) = cos(x)
Range is [-1,1], codomain is R

Question 8

Difference between derivative function and first order condition?

Answer 8

Derivative is a mathematical function, obtained through differentiation

FOC is an EQUATION, a statement about the dedicate of the objective function, that defines the critical point x*

Question 9

What is a a critical point?

Answer 9

A point that is a solution of the FOC

Question 10

What is R(+)?

Answer 10

Set of all non-negative real numbers tf including 0

Question 11

Difference between strictly convex/concave and convex/concave functions?

Answer 11

For strictly, the second derivative must be > or < 0, for not it is just greater/less than or equal to 0 for all x is a set of R