2 An individual's utility function is given by U = x;X2 where x, and x, denote the number of items of two goods, G1 and G2. The prices of the goods are $2 and $10 respectively. Assuming that the individual has $400 available to spend on these goods, find the utility-maximizing values of x, and x2. Verify that the ratio of marginal utility to price is the same

Which of the following statement is TRUE Group of answer choices As the consumption of a good increases, marginal utility rises, but total utility falls. As the consumption of a good increases, total utility falls and marginal utility falls. As the consumption of a good increases, total utility rises, but marginal utility falls.

U(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.

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 på and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity. (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and Py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px 10, 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 and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y> 0). =