# What is the utility function for perfect complements?

## What is the utility function for perfect complements?

The utility that gives rise to perfect complements is in the form u(x, y) = min {x, βy} for some constant β (the Greek letter “beta”). First observe that, with perfect complements, consumers will buy in such a way that x = βy.

## What are examples of perfect complements?

Example: Right shoe and left shoe. You need exactly one right shoe with every left shoe. The indifference curves for perfect complements will always be right angles.

Which type of isoquant curve is observed in case of perfect complements?

If the two inputs are perfect complements, the isoquant map takes the form of fig. B; with a level of production Q3, input X and input Y can only be combined efficiently in the certain ratio occurring at the kink in the isoquant. The firm will combine the two inputs in the required ratio to maximize profit.

### How do you find optimal utility?

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.

### What is ISO quant curve?

An isoquant curve is a concave line plotted on a graph, showing all of the various combinations of two inputs that result in the same amount of output. Most typically, an isoquant shows combinations of capital and labor and the technological trade-off between the two.

What is smooth isoquant?

Smooth Convex Isoquant The isoquant in which there can be only two possible combinations say A and B, except this the two factors of production are incapable of substituting each other. Thus a smooth convex curve is formed from A to B.

## Why the ISO quant curve is convex to the origin?

An isoquant must always be convex to the origin. This is because of the operation of the principle of diminishing marginal rate of technical substitution. MRTS is the rate at which marginal unit of an input can be substituted for another input making the level of output remain the same.

## What is the MRS for perfect substitutes?

For perfect substitutes, the MRS will remain constant. Lastly, the third graph represents complementary goods. In this case the horizontal fragment of each indifference curve has a MRS = 0 and the vertical fractions a MRS = ∞.

What is the condition for optimal choice?

The optimal choice from a combination of goods is attained when all income is spent, and the consumer is on the highest attainable indifference curve. In other words, the optimal choice is attained when the budget line is tangent to the indifference curve.

### Do perfect complements have MRS?

MRS for perfect complements is same along a vertical or horizontal strip, while it is not defined at the kink. In case of perfect substitutes, MRS is same along the entire indifference curve.

### How do you find the utility function of perfect complements?

The general form of the utility function in case of perfect complements is: where k 1 and k 2 are positive numbers indicating the proportions in which x 1 and x 2 are consumed, i.e., k 1 = p 1 x 1 /m, k 2 = p 2 x 2 /m and k 1 + k 2 = 1.

What is isoelastic utility?

Isoelastic utility. In economics, the isoelastic function for utility, also known as the isoelastic utility function, or power utility function is used to express utility in terms of consumption or some other economic variable that a decision-maker is concerned with. The isoelastic utility function is a special case…

## What is a U utility function in economics?

Utility functions are expressed as a function of the quantities of a bundle of goods or services. It is often denoted as U (X 1, X 2, X 3, X n). A utility function that describes a preference for one bundle of goods (X a) vs another bundle of goods (X b) is expressed as U (X a, X b).

## What is the isoelastic utility function of CRRA?

The isoelastic utility function is a special case of hyperbolic absolute risk aversion and at the same time is the only class of utility functions with constant relative risk aversion, which is why it is also called the CRRA utility function. It is. u ( c ) = { c 1 − η − 1 1 − η η ≥ 0 , η ≠ 1 ln ⁡ ( c ) η = 1.