Assume you have $100 to spend on two goods, X and Y. You also know that your utility is given by the equation U=XY+ 10X. a. Assume that the prices of X and Y are each $1. Set up a Lagrangian and find your optimal consumption bundle. b. If the price of good X rises to $5, what is the new optimal bundle? What is the total effect of the price change on the consumption of each good? c. Use a Lagrangian to find the substitution effect of the increase in the price of good X on the consumption in each good. What income would you need in order to attain. your original level of utility when the price of X rises to $5? d. What is the income effect of the price increase? Are X and Y normal or inferior? Explain your answer. e. Show that the total effect you found in part b is equal to the sum of the substitution and income effects you found in in part c and d.