4. Irene's likes to consume exactly two packets of sugar (X1) with each cup of coffee. Initially, each packet of sugar costs p1 = $0.20 (20) and each cup of coffee costs 292 = $1. Irene has $252 to spend on coffee (with sugar). 3) b) C) Write down Irene's utility function. Derive her demand function for X1 as a function of M and p1. How many packets of sugar and cups of coffee will Irene buy at the given prices and income? What is her utility level at this consumption? Now the government imposes a per unit tax of t = $0.02 (2) on each packet of sugar. As a result, sugar packets now cost pf\" = $0.22 (22). How does this change Irene's consumption of coffee and sugar? What is the Compensating Variation that will make Irene as well off as before the tax? Use your answer to part f) to separate out the income and substitution effects of the per-unit tax on the demand for sugar