Please solve this question

3. Answer: (a) What is the compensating variation? What is the equivalent variation? What is the difference between them? (b) You consume two goods, good x and good y. These goods sell at prices Pr = 1 and Py = 1, respectively. Your preferences are represented by the following utility function: U(x, y) = x + In(y). You have an income of m = 100. How many units of x and y will you buy and what will is your utility? If Pr increases from $1 to $2, figure out the compensating variation (CV) associated with price change. (c) If instead your utility is U(x, y) = In(x) + y, figure out the com- pensating variation (CV) as Pr increases from $1 to $2. (d) Are the compensating variations the same for both of the above utility functions? Explain your answer rigorously