2. [Application: Labor supply and fertility problem] Consider a consumer's decision problem in having to allocate her time between working, leisure and having children. This individual is endowed with T units of time which she can divide between working (h), her own leisure (1) and children. The hourly wage rate is w; therefore, if she works h hours, her labor income is wh. Additionally, she also receives an allowance I from her wealthy father. She uses this total income to purchase a good x for her own consumption which is priced at p per unit. Having and rearing each child requires a time commitment of t, plus c units of the consumption good. Assume that her preferences over her own consumption x, her own leisure 1, and children n are given by the following utility function: u(x, l, n) = log(va + v+ avn), (i) Write the consumer's optimization problem with the appropriate re- source constraints, and derive the amount of labour she supplies in the market. (ii) When may this individual decide not to work at all?