**Questions 1. **Ben’s preferences over coke, ????1 and pizza, ????2 can be summarized by the utility function, ????(????1, ????2 ) = ????1 2????2.a) Find the marginal utilities of coke and pizzab) Calculate the MRS c) Find the Marginal Rate of Transformation (MRT) d) Calculate the optimal quantity of coke and pizza consumption as a function of ????1, ????2 and ????.e) Illustrate the optimal bundle when ????1 = 2, ????2 = 10 and ???? = 180.f) What is the numerical value this utility function?**Question 2. **Refer to question 2 above. The government imposes a tax rate of 25% on the price of coke,a) Show that the tax rate is equivalent to a price increase to a consumerb) Sketch the original budget constraint and the new budget constraint on the same graph. Label the graph appropriately.c) What is the effect of the price increase on the consumption of ????1?d) What is the effect of the price increase on real income if the tax is applied on both goods?**Question 3. **A consumer with a certain income has to choose between different quantities of ????1 and ????2 in such a way that he maximizes his utility. If the price of ????1 falls, we get two different effects.a) What do we call the two effects?b) With the aid of a graph distinguish between the two effects.