Question 2 - Consider a consumer with utility function U = x1 + x2 12, where is the labor supplied, x₁ and x2 are the quantity of consumption for good 1 and 2 respectively. The price of good 1 and 2 are p₁ and p2 respectively (P1, P2 > 0). The consumer cannot spend more than its earning from working, and has no other source of income. The consumer has an hourly wage rate of w. In the short-run, the consumer has signed a work contract that the work hour is fixed at ī> 0. The consumer cannot consumer negative amount of quantity of goods. a) Write down the constraints faced by the consumer in the short run. b) Find the utility maximising quantity of consumption for good 1 and 2 in the short run. Assume p₁ > P₂• c) In the long run, the consumer could choose the labour supply 1, i.e. I is not fixed and is a choice for the consumer. The consumer cannot work more than 24 hours a day, and cannot work negative amount of hours. Find the utility maximising quantity of consumption and labour supply. Assume p₁ > P2 and w< 48p2. d) What are the economic assumption(s) implicit in the model? Discuss if they are reasonable assumptions.