QVideo. Please answer to the question below in a short video about 5 minutes. You will need to submit the link to your video via the appropriate submission link on the KEATS page.

Explain clearly and in detail, the steps you take to reach the solution.   In particular, explain how you set up the question, why you do what you do in each step.  For example,  “In this question, we find the optimal levels of consumption of good 1 and good 2 that will maximise the utility of X, which is given by the function, subject to the following budget constraint.  In order to solve this optimisation question, we start by writing the Lagrangian function by doing x and y. Then, we check the first- order conditions...  etc”.  The goal here is for you to describe what you are doing and why. You could skip the steps involving manipulation of equations to reach parts of the solution.  State clearly your key findings.  For example,  “By using equation (1) and (2) we can find that the optimal consumption level of good 1 is a and that of good 2 is b”. Discussion and explanations are as important as the solution itself.

Question: An individual works and spends 25 % of their income on housing. The rest is split between two goods x1 and x2 . Their utility is given by U = x1(2)  + x2(2) .

(a) If they work for 40 hours a week and they need to work for 2 hours to afford 1 unit of x1  and 1 hour for 1 unit of x2 .  Write the constraint they are facing and find the optimal consumption bundle that maximises utility using a Lagrangian function. How do you interpret the results? (50 points).

(b) Prices change and now they only need 1 hour for 1 unit of x1 .  Discuss how this would change the optimal bundle.(30 points)

(c) Imagine they get a promotion, which increases the hourly wage by 50%.   Discuss how that would change the opti- mal consumption bundle in absolute and relative terms (20 points)