Is expenditure function concave?
The expenditure function is given by the lower envelope of {ηx1,x2 (p1) : u(x1,x2) = u} Since the minimum of linear functions is concave, the expenditure function is therefore concave.
How do you invert an expenditure function?
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- The expenditure function is the inverse of the indirect utility function with respect. to wealth w:
- v(p, e(p, u)) = u. In this case, applying the above formula is enough to get the result:
- e(p, u) p1 + p2.
What are the properties of expenditure function down?
In microeconomics, the expenditure function gives the minimum amount of money an individual needs to spend to achieve some level of utility, given a utility function and the prices of the available goods.
What is the Cobb Douglas demand function?
There are several classes of utility functions that are frequently used to generate demand functions. One of the most common is the Cobb-Douglas utility function, which has the form u(x, y) = x a y 1 – a. Another common form for utility is the Constant Elasticity of Substitution (CES) utility function.
Why is expenditure function homogeneous of degree 1?
Theorem: If u(x) is continuous, strictly quasi-concave and non-satiated, then the associated cost (expenditure) function c(p, u) is homogeneous of degree 1 in p, concave, strictly increasing in u, and has partial derivatives which are the compensated (Hicksian) demand functions.
Why is Hicksian demand downward sloping?
Hicksian: yes. In a two good case, the assumption that marginal rates of substitution are declining assures that Ilicksian demand is downward sloping. (Since Hicksian demand traces out consumer decisions along a fixed indifference curve as the own good price, and hence the price ratio, change). 2.
What does homogeneous of degree mean?
For example, a function is homogeneous of degree 1 if, when all its arguments are multiplied by any number t > 0, the value of the function is multiplied by the same number t.
What does it mean to be homogeneous of degree zero?
HOMOGENEOUS OF DEGREE ZERO: A property of an equation the exists if independent variables are increased by a constant value, then the dependent variable is increased by the value raised to the power of 0. In other words, for any changes in the independent variables, the dependent variable does not change.
How do you find the expenditure function from Hicksian demand?
Hicksian demand is the derivative of the expenditure function. ∇p e(p, v) = h∗(p, v) − 0 since F does not depend on p. Walrasian demand equals the derivative of the indirect utility function multiplied by a “correction term”. This correction normalizes by the marginal utility of wealth.
Is Cobb-Douglas production function homogeneous?
The Cobb-Douglas is homogeneous of degree = (+ ).
What is special about Cobb-Douglas?
The Cobb–Douglas production function is especially notable for being the first time an aggregate or economy-wide production function had been developed, estimated, and then presented to the profession for analysis; it marked a landmark change in how economists approached macroeconomics from a microeconomics perspective …
What is a homogeneous function of degree zero?
Is Cobb Douglas homogeneous?
Examples of linearly homogeneous production functions are the Cobb-Douglas production function and the constant elasticity of substitution (CES) production function.