Suppose that Lizzie has a toddler (Benjy). Benjy is a "busy" boy and Lizzie is ...

At present, because of her reticence to leave Benjy in the care of others, Lizzie has very steep indifference curves.  She would have to be compensated with a large increase in income if she were to reduce her time at home.  As a consequence, it's likely that Lizzie does not participate in the labor force at present.  As Benjy ages and becomes less of a handful, we would predict that Lizzie's indifference curves will flatten out as her household production time becomes less of a necessity.  As this happens, it will become more likely that Lizzie's optimal income/household time choice incorporates some time spent working for pay.