## Which of the following utility functions is an example of Cobb-Douglas preferences?

Which of the following utility functions is an example of Cobb-Douglas preferences? utility of clothing.

## What are the properties of Cobb-Douglas production function?

The powers of labor and capital (that are β and α) in the C-D production function measure output elasticities of labor (L) and capital (K) respectively. The output elasticity of a factor shows the percentage change in output due to a given percentage change in the number of factor inputs.

**What is Cobb-Douglas preferences?**

Cobb-Douglass preferences are one of the simplest algebraic representations of well-behaved preferences. 2. Cobb-Douglas Preferences. Assume the consumer’s utility function is given by: u x1,x2.

**Is MRT same as MRS?**

The Difference Between the MRT and the Marginal Rate of Substitution (MRS) While the marginal rate of transformation (MRT) is similar to the marginal rate of substitution (MRS), these two concepts are not the same. The marginal rate of substitution focuses on demand, while MRT focuses on supply.

### How do you derive 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.

### How do you know if a function is Cobb-Douglas?

Production Functions A Cobb-Douglas Function takes the form of Q=KαLβ where Q=output, K=capital, L=labour, and alpha and beta are used to represent input shares of capital and labour respectively. In this form we have used CD as a production function.

**What is the slope of Cobb-Douglas production function?**

For the production function, the slope is the marginal product of one of the two factors, holding the other con- stant. Using calculus, the slope is simply the partial derivative of the Cobb- 2 Page 3 Douglas function with respect to X holding Y constant, or vice-versa.

**What is the property of Cobb-Douglas production function?**

The sum of the powers/exponents of factors in Cobb-Douglas production function, that is α+β measures the returns to scale. Therefore, If α+β=1, it exhibits constant returns to scale (CRS) If α+β>1, it exhibits increasing returns to scale (IRS)

#### Why does MRT increase?

Answer and Explanation: MRT increases because generally a PPC is concave to the origin.

#### What is the difference between MRT and MRS?

**Why is MRT MRS optimal?**

For all consumers, MRS=MRT must be true. The consumer’s utility is maximized at the bundle where the rate at which the consumer is willing to trade one good for the other equals the rate at which she can trade. It also implies that MRS for all consumers is the same. For all producers, MRTS must be the same.

**What is the difference between MRT and MOC?**

Answer: MRT is the ratio of loss of output y to gain output x interms of unit and MOC is the ratio of unit sacrifice to gain additional unit of another good in terms of money.

## Is Cobb-Douglas Homothetic?

Linear utilities, Leontief utilities and Cobb–Douglas utilities are special cases of CES functions and thus are also homothetic.

## What is an example of Cobb Douglas utility function?

Cobb-Douglas Utility Functions with Many Goods The Cobb-Douglas utility function can easily be extended to any number of goods; for example, u (x_1,x_2,x_3) = x_1^ax_2^bx_3^c u(x1,x2

**What is Cobb-Douglas utility?**

Cobb–Douglas utilities. The Cobb–Douglas function is often used as a utility function. In this context the consumer is assumed to have finite wealth, and utility maximization takes the form: where is the total wealth of the consumer and are the prices of the goods. The utility may be maximized as follows.

**What is the significance of the Cobb-Douglas production function?**

These equations highlight the role of the parameterb, which deter- mines the share of capital and labor in total output. In general these shares are approximately constant in most real economies and this makes the Cobb-Douglas production function a good approximation.

### How do you find the Cobb-Douglas function?

Assuming perfect competition and α + β = 1, α and β can be shown to be capital’s and labor’s shares of output. In its generalized form, the Cobb-Douglas function models more than two goods. The Cobb–Douglas function may be written as: f ( x ) = A ∏ i = 1 L x i λ i , x = ( x 1 , … , x L ) .