1) Problems and Applications Q4 Between January 2012 and January 2019, U

1)That statement is False

A labor force is defined as to observe an increase if and only if the amount of people emplyed grow in larger number when compared to the amount of unemployed people in a perticular period.
In this case,
17.3 million - 6.3 million = 4.8 increase in labor force.

The labour force is just defined as the individuals who are wanting and are ready to accomplish the work. The measure of the work force or labour force is commonly used to discover the unemployment of a firm.

The mentioned answer is correct mentioned.

2)

Utility function is a way of assigning a number to every possible consumption bundle such that more preferred productss get assigned larger numbers than less-preferred products. Preference is the order that a person (an agent) gives to alternatives based on their relative utility, a process which results in an optimal "choice" (whether real or theoretical

Now it is to be seen whether we can take preferences and map them to some sort of utility index. If we can somehow represent preferences by such a function we can apply mathematical techniques to make the consumer’s problem more tractable. Working with preferences directly requires comparing each of a possibly infinite number of choices to determine which one is most preferred.

A utility function u : X → R represents preference relation t if, for all x, y, x t y ⇔ u (x) ≥ u (y )

Only rational preferences relations can be represented by a utility function. Conversely, if X is finite, any rational preference relation can be represented by a utility function.

Given two goods, x and y, the agent weakly prefers x over y if x is at least as good as y. To avoid us having to write “weakly prefers” repeatedly, we simply write x < y. We now put some basic structure on the agent’s preferences by adopting two axioms.

In turn, a utility function tells us the utility associated with each good x ∈ X, and is denoted by u(x) ∈ < y (1.1) This means than an agent makes the same choices whether she uses her preference relation,

x y: x is preferred strictly to y.

x ~ y: x and y are equally preferred.

x y: x is preferred at least as much as is y

x y: x is preferred strictly to y.(x y: x is preferred strictly to y y: x and y are equally preferred.( x ( ( x y: x is preferred at least as( much as is y ~ ( much as is y.

A utility function U(x) represents a preference relation if and only if: preference relation if and only if:( x ’ x ” U(x ’) > U(x ” ) ~ ( ( x ’ x ” U(x ’ ) > U(x ” ) ( x’ x” U(x’) < (U(x”) x’ x” U(x’) = U(x”)(

A utility function U(x) represents a preference relation   

A utility function U(x) represents a preference relation if and only if:

Equal preference have the same utility level.(

x’ x” U(x’) > U(x”)

x’ x” U(x’) < U(x”)

x’ ~ x” U(x’) = U(x”).

So if there are two sets of goodsU (X,Y)=X and U(X,Y) =Y then the indifference curve with the utility level X but the bundle or product with utility level U(X,Y) =Y will have different utility level .

On the indifference curve it will be plotted differently on a vertical axis.

So comparision of two products will create a better description of the consumer’s preferences.

The complete collection of indifferences represent the consumer’s preferences and an indifference map is equal to utility

please see the attached file for the complet solution.

3)

22):-It is true

as we know that at the medium run equilibrium unemployment rate is equal to natural rate of unemployment and at the natural rate of unemployment realized inflation is equal to the expected inflation and we all know that inflation neither fall or rise so at natural rate of unemployment so at the medium equilibrium it is stable

Sorry for 21