# Is quasilinear concave?

## Is quasilinear concave?

This is called a quasi-linear function because utility is linear in c and some function of t. Thus v″(t)<0: v is a concave function. Because indifference curves are of the form ′c=constant−v(t)′, any two of them differ by a constant vertical distance, as you can see in Figure 1.

### How do you know if a utility function is quasilinear?

In other words: a preference relation is quasilinear if there is one commodity, called the numeraire, which shifts the indifference curves outward as consumption of it increases, without changing their slope.

#### How do you graph an indifference curve with a utility function?

If you are given a utility function U(x,y), it is easy to derive a given indifference curve from it: simply plot all points (x,y) such that U(x,y) equals a constant. This is a utility function in which the consumer values x as much as a/b units of y.

Is quasilinear convex?

A characteristic feature of quasi-linear preferences is that they are not strictly convex. Under such preferences, the existence and uniqueness of an interior optimal allocation is not, in general, guaranteed.

What is quasilinear equation?

Quasilinear equation, a type of differential equation where the coefficient(s) of the highest order derivative(s) of the unknown function do not depend on highest order derivative(s)

## How is MUx calculated?

To find the consumption bundle that maximizes utility you need to first realize that this consumption bundle is one where the slope of the indifference curve (MUx/MUy) is equal to the slope of the budget line (Px/Py) in absolute value terms. You know MUx = Y and MUy = X, so MUx/MUy = Y/X.

### Are quasilinear goods essential?

And, an individual is indifferent to any bundle that contains both goods (like bundle E) only if the second bundle also contains some of both goods. In that sense, both goods are quite essential to the well-being of the individual. 8 True or False: Quasilinear goods are never essential.

#### Why is the utility function in commodity 1 quasilinear?

In two dimensional case, the indifference curves are parallel; which is useful because the entire utility function can be determined from a single indifference curve. A utility function is quasilinear in commodity 1 if it is in the form

Do quasi-linear indifference curves have Mrs’s that depend on the nonlinear variable?

Do quasi-linear indifference curves have MRS’s that depend only on the nonlinear variable? For example, for a U (x) = √ (x) + y, I calculated that the y would not be in the MRS. Does that mean that a consumer does not factor the consumption of a “linear” good y into their utility maximization?

How is quasilinear utility used in mechanism design?

In mechanism design, quasilinear utility ensures that agents can compensate each other with side payments. All the indifference sets are parallel displacements of each other along the axis of commodity 1.

## When is a preference relation a quasilinear relation?

In other words: a preference relation is quasilinear if there is one commodity, called the numeraire, which shifts the indifference curves outward as consumption of it increases, without changing their slope.