1. State whether the following statements are True (T) or False (F) (

a) Every quasiconcave function is concave function but every concave function is not a quasi concave function.

(b) Consider an objective function f(x1, x2, .., xn) and constraint g(x1, x2, .., xn) = 0. At the optimum, it is not necessary that f1/g1 = f2/g2 = fn/gn where fi and gi are the partial derivatives of f and g w.r.t. xi

(c) Given a budget set pX.X + pY .Y = I, where I is income, spent on goods X and Y costing px and pY respectively. Assume that the Utility function is such that the indifference curves are convex but touch the X-axis (refer figure 4.4 pg 120). If the ratio of relative prices pX/PY is < (less than) UX/UY , then NO corner solution is possible

(d) The indirect utility function is homogeneous of degree 0 in income and prices

(e) Lexicographic preferences are similar to words in a dictionary. If a consumer has lexicographic preferences, then given 2 goods x and y, the consumer always prefers any combination of goods as long as x > y. If x is food and y is clothing and the consumer has preferences as described above, it imples that these preferences cannot generate a continuous utility function or indifference curves

(f) Homothecity property implies that for a given price ratio (pX/pY ) the behaviour (ratio of x to y) of rich (higher indifference curve) and poor (lower indifference curve) are the same

(g) If u is a utility function representation of and f is any other function with domain and range of real numbers, then v defined by v(x) = f(u(x)) is another utility-function representation of

(h) Quasi-concavity of the utility function is not necessary for the preferences to be convex 1 (i) If the covariance between 2 variables is 0 it implies they are independent and if the variables are independent then the covairance between them is 0 (j) Expenditure functions are convex in prices