Question [3]: As discussed, a consumer could also have an endowment, instead of income.
For each of the following utility functions, what is the Demand function for a consumer facing
price vector ($p_1, p_2$) if the consumer has the endowment vector ($w_1, w_2$) = (10, 5). (Hint: this
should not take long at all.)
1. (Cobb Douglas) $u(x) = x_1^{0.4}x_2^{0.6}$.
2. (quasi-linear) $u(x) = x_1 + 10 \ln x_2$
3. (perfect substitute) $u(x) = 3x_1 + x_2$
4. (Leontief) $u(x) = \min\{2x_1, x_2\}$