José Maria's utility function is U(B, Z)=A B^α Z^β What is his marginal utility of B ? What is h

step 1 So while seeing the question, let's further move to the answer. So let's see here that U is equa

José Maria's utility function is U(B, Z)=A B^α Z^β What is...

José Maria's utility function is $U(B, Z)=A B^{\alpha} Z^{\beta}$ What is his marginal utility of $B$ ? What is his marginal utility of $Z$ ? What is his marginal rate of substitution between $B$ and $Z$ ? $C$

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Key Concepts

Utility Function

A utility function is a mathematical representation of a consumer's preferences that assigns a level of satisfaction or utility to different bundles of goods. It is used to analyze choices and trade-offs between different goods in economic theory.

Marginal Utility

Marginal utility measures the additional satisfaction a consumer gains from consuming an extra unit of a good. It is obtained by taking the partial derivative of the utility function with respect to that good, holding the consumption of other goods constant.

Partial Derivative

A partial derivative is a derivative taken with respect to one variable while treating other variables as constants. In the context of utility functions, it is used to calculate how the utility changes as the quantity of one good changes, which yields the marginal utility.

Marginal Rate of Substitution

The marginal rate of substitution (MRS) is the rate at which a consumer is willing to give up units of one good in exchange for additional units of another good, while keeping the total utility constant. It is calculated as the ratio of the marginal utilities of the two goods.

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