What is expenditure minimization economics?

What is expenditure minimization economics?

The expenditure minimisation problem (EMP) looks at the reverse side of the utility maximisa- tion problem (UMP). The UMP considers an agent who wishes to attain the maximum utility from a limited income. The EMP considers an agent who wishes to find the cheapest way to attain a target utility.

What is the dual problem of minimum expenditure function?

Consumer’s dual problem: minimizing expenditure subject to a utility constraint (i.e. a level of utility the consumer must achieve). The dual problem yields the “expenditure function,” the minimum expenditure required to attain a given utility level.

How do you solve for expenditure function?

To derive the expenditure function we can either (i) invert V and solve for M, or (ii) set up the dual of the consumer’s choice problem, solve for Hicksian demand functions and substitute them into the objective (i.e., expenditure) function.

What is minimum expenditure function?

From Wikipedia, the free encyclopedia. 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.

How do you go from indirect utility to expenditure function?

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1. The expenditure function is the inverse of the indirect utility function with respect. to wealth w:
2. v(p, e(p, u)) = u. In this case, applying the above formula is enough to get the result:
3. e(p, u) p1 + p2.

Why expenditure function is concave in prices?

(b) Intuitively explain why the expenditure function is concave in prices. 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.

What is meant by dual problem in context of the utility and expenditure Optimisation exercise?

The dual problem in context of the context of the utility and expenditure optimization is to increase the utility of the goods depending on the primal demand along with minimization of the costs involved during the period of dual demand.

Why expenditure function is 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.

Why is expenditure function homogeneous of degree 1?

βi i . γij log(pj) + βi log(y/P). 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.

What is the problem of expenditure minimization in microeconomics?

Expenditure minimization problem. In microeconomics, the expenditure minimization problem is the dual of the utility maximization problem: “how much money do I need to reach a certain level of happiness?”. This question comes in two parts. Given a consumer ‘s utility function, prices, and a utility target, how much money would…

How is the expenditure minimization problem related to utility maximization?

In microeconomics, the expenditure minimization problem is the dual of the utility maximization problem: “how much money do I need to reach a certain level of happiness?”. This question comes in two parts. Given a consumer ‘s utility function, prices, and a utility target,

Is the expenditure function dependent on the level of utility?

We could write M = E (U,Px,Py) which just says that the expenditure (income required) to gain the level of utility is dependent on the level of utility you are trying to attain and the price of goods. Sorry, that was long and tedious. However, that is the expenditure function.

How is an expenditure function defined in economics?

Expenditure function. Formally, the expenditure function is defined as follows. Suppose the consumer has a utility function defined on commodities. Then the consumer’s expenditure function gives the amount of money required to buy a package of commodities at given prices that give utility of at least ,