please provide explanation

3. The lump sum principle illustrated in lecture 8 applies to transfer policy and taxation. This problem examines this application of the principle. (a) Use a graph similar to the graph in lecture 9 to show that an income grant to a person provides more utility than does a subsidy on good x that costs the same amount to the government. (b) Use the Cobb-Douglas expenditure function presented in Lecture 8 to calculate the extra purchasing power needed to increase this person's utility from U = 2 to U= 3. Expenditure function is E(Pz, Py, U) = 2Px Py U (3) suppose Pr = 1, Py = 4 and income I = 8. (c) Use Expenditure function (Equation (3)) again to estimate the degree to which good x must be subsidized to increase this person's utility from U = 2 to U = 3. How much would this subsidy cost the government? How would this cost compare with the cost calculated in part (b) ? (d) Question 2 asks you to compute an expenditure function for a general Cobb-Douglas utility. Now,use that expenditure function to re-solve parts (b) and (c) here for the case a = 0.3. fraction of income that low-income people spend on food. (e) How would your calculations in this problem have changed if we had used the expenditure function for the Perfect Complements case instead? Say the expenditure function for the Perfect Complements case is E(Pz, Py, U) = (Pr + 0.25p,)U (4)