L.N. Gumilyov Eurasian National University

BUS 405

Note: Write substantive answers, in whatever style you consider the most ef-
fective: do not try to fill in space with aimless speculation. The grading function
is symmetric and additively separable over questions, and it is convex. You are
expected to upload your answers as a single file to Moodle.
Important: Feel free to discuss questions with each other, but you are not
allowed to solve the questions together. You need to write down your own original
answers. Plagiarism will result in failure from the class and making same mistakes
in a similar order will be judged as plagiarism.
1. Revisiting In-Class Exercise: Suppose a worker chooses consumption, C,
and leisure, l, to maximize the utility function
U (C, l) = α (C − c0)ρ − 1
ρ + (l − l0)τ − 1
τ
subject to the budget constraint C = w(T − l) + μ, where T is the time endowment,
w is the real wage and μ is the non-labor income. It is assumed that ρ < 1, τ < 1,
μ > c0, and T > l0.
a)
M Ul = ∂U (C, l)
∂l = τ (l − l0)τ −1
τ = (l − l0)τ −1
M UC = ∂U (C, l)
∂C = α ρ(C − c0)ρ−1
ρ = α(C − c0)ρ−1
w = M Ul
M UC
= (l − l0)τ −1
α(C − c0)ρ−1 = (C − c0)1−ρ
α(l −