Let’s say we extend the the standard 1 person static labor supply problem instead to a family with two people making money. In the family of two money makers, given as person 1 and person 2, the given utility function is u(c1 + c2, l1, l2). Utility is defined as a function of the sum of goods consumed by the two people in the family, and of each person’s leisure time. Each person has a time endowment of “Ti” and gets a wage “wi”, where i = 1, 2. The two person family has a non-labour income defined y (which means this is the income of the family whether or not they work) and face price “p” for consumption goods. How can I utilize the Slutsky equation to show how the labour supply of 2 changes with w1?

ENGR.ECONOMIC ANALYSIS
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Let’s say we extend the the standard 1 person static labor supply problem instead to a family with two people making money.

In the family of two money makers, given as person 1 and person 2, the given utility function is u(c1 + c2, l1, l2).

Utility is defined as a function of the sum of goods consumed by the two people in the family, and of each person’s leisure time. Each person has a time endowment of “Ti” and gets a wage “wi”, where i = 1, 2.

The two person family has a non-labour income defined y (which means this is the income of the family whether or not they work) and face price “p” for consumption goods.

How can I utilize the Slutsky equation to show how the labour supply of 2 changes with w1?

Thank you!

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