ti] Consider the following statements and say whether they are true or false and why. Provide clearjustiftcation iii. iv. vi. vii. viii. ix. for your answers. {26' marks} If two goods are perfect complements and the price of one of them increases. the quantity demanded of both goods decreases. A. non-transitive preference relation .1: can be represented by some utility function. Consider two goods it. and y. if preferences are strictly convex. the absolute value of the marginal rate of substitution between it and y is decreasing along an indifference curve as it increases. The following Cobb-Douglas utility functions represent two different preference relations: U: {L y) = [1.3 logtx] + 0.6 logty] U: (x. y} = Il logix] + 1.2 logiy]. If a consumer is making an optimal choice between two goods it and y, then, independently of his preferences. the following condition must always hold: fhrfpy} = MRS fr. y}. [f the following condition holds fprx'pygt = MR3 fir. _i;l then a consumer must be making the optimal choice between it and y. independently of his preferences. A cigar is a luxury good fora consumer that has Cobb-Douglas preferences over cigars and food. Consider two goods )t'. and y. with prices pr and py. respectively. A ill)? percent value tax on these two goods does not affect the relative price ofx in terrns of y. The marginal rate of substitution measures the rate at which the market is willing to substitute one good for the other. An indifference curve represents the collection ofall the bundles that a consumer can buy