Suppose a student consumes two goods, snack (k) and stationery (y) and has utility function U(k,y)=ky. She has a budget of R400. The price of snack is Pk =10 and the price of y is Py=20 1.1. Find her optimal consumption bundle using the Lagrange method. [8] 1.2. Show what happens to optimal bundle when there is a snacks' special, with Pk=5 all other things remaining constant? [4] 1.3. Derive constrained and unconstrained demand curves for the individual on snacks. You can make any additional assumption over and above the ones in question (ii). [18] 1.4. Assuming that utility derived with optimal values in question (i) is 200 utils and that the drop in prices in all probability increases utility by 50% Compute the amount of compensation required, if any. Explain clearly with use of examples the nature of compensation, and motivate why that amount is best compared to alternatives. [10]