21. A consumer has a utility function defined over two goods X and Y. Let the quantity ofGood X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is givenbelow:u(x, y) = xy + 2y.Assume that the consumer has income m and that prices are på and py.(a) Explain whether the preferences underlying this utility function satisfycompleteness and transitivity.(b) Explain whether the preferences underlying this utility function satisfymonotonicity and convexity.(c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0and Py> 0.(d) Show that goods X and Y are normal goods and explain whether either good is asubstitute for the other.(e) Assume that px10, Py= 5 and m = 100. Suppose that px increases to px = 15,how much of the change in demand for Good X is via the substitution effect andhow much is via the income effect?Note: You may assume an interior solution (i.e. x > 0 and y> 0).=

A utility function is a mathematical representation that quantifies an individual's or a…

21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are px and Py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity.