HomeProductivity

# HomeProductivity - Home Productivity and the Two Person...

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Home Productivity and the Two Person Household 1 The Basic Setup This handout will focus on the model where the household labor supply decisions of two individu- als are simultaneously made by one entity. Let there be two goods - home goods ( HG ) and market goods ( MG ), created via home production and market production, respectively. Both goods yield positive utility for the household. Every individual has some rate of home production we’ll call H . They also have a rate of market production, which is the wage W they earn for each hour of work. Table 1: Household and Market Production rates Household Production Market Production Individual 1 H 1 W 1 Individual 2 H 2 W 2 We can graph Individual 1’s budget set in HG/MG space, as shown in Figure 1. MG HG Slope = " W 1 H 1 T*H 1 T*W 1 Figure 1: Example budget set for Individual 1 The budget set represents all possible combinations of market and home goods Individual 1 can Prepared by Nick Sanders, UC Davis Graduate Department of Economics 2006

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produce with some allocated time T . The slope of the line represents the rate of exchange between home production and market production, which I’ll refer to from here on as the ”productivity ratio”. For each hour of work Individual 1 takes away from home production and puts toward market production, they lose H 1 in HG and gain W 1 in MG. A similar graph could be made for Individual 2. Now let’s assume these two individuals live together - what is the household budget set? Say the decision is that both individuals will always allocate their hours in the same way (both spend α time on home production and T - α in the labor market). Then the budget set will be a straight line with a slope equal to - W 1 + W 2 H 1 + H 2 , as shown in Figure 2. Here the max possible home production is T * ( H 1 + H 2 ) , the max market production is T * ( W 1 + W 2 ) , and the budget set has a constant slope throughout. MG HG Slope = " W 1 H 1 T*H 1 T*W 1 MG HG Slope = " W 1 + W 2 H 1 + H 2 T*( H 1 +H 2 ) T*( W 1 +W 2 ) Figure 2: Example budget set - joint household with identical time allocation between individuals If there is any differential in productivity ratios between the two individuals, the household can maximize their budget set by changing their work allocation strategy, and having at least one person specialize in either home or market production. For example, let
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## This note was uploaded on 04/21/2008 for the course ECON 151A taught by Professor Miller during the Fall '06 term at UC Davis.

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HomeProductivity - Home Productivity and the Two Person...

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