a) What do you understand by the concept of marginal utility? [2 Marks] b) What do you understand by the concept of a diminishing marginal rate of substitution? [2 Marks] c) If the total utility function of an individual takes the form : U(x,y) = ( + 2) 2 ( + 3) 2 where U is the total utility and x and y are the quantities of the two goods; (i) Find the marginal utility function of good ''x'' [3 Marks] (ii) Find the marginal utility function of good ''y'' [3 Marks] (iii) Find the value of the marginal utility of good ''x'' when 4 units of each good are consumed. [3 Marks] (iv)Find the marginal rate of substitution function for the above total utility function. [3 Marks] (v) Is the total utility function above convex or not? [3 Marks] d) The demand function of a good ''x1'' is given by Px1 = 8,000 - 24x1. Using definite integral calculus, find the consumer surplus for the individual when he consumes 100 units of good ''x1'' [3 Marks] e) The supply function of a good ''x2'' is given by Px2 = 1,800 + 0.03 (2 ) 2 . Using definite integral calculus, find the producer surplus for the producer when he/she sells 50 units of good ''x2''