2. Mark has preferences between guns and banjos that are described by the utility function u(a:g, :35) = mg + (37b)1/2 _ (a) Write down the equation for an indierence curve (i.e. for some utility u,write down the number of guns as a function of the number of banjos) (b) Using this indi'erence curve, determine whether these are convex? (c) Write down an equation for the marginal rate of substitution of banjos for guns. (1 Show that, for a budget constraint 3351);, + p m = m, at any point of tangency between budget line and 9 g 2 indifference curves it must be the case that :35 = % (lgf) (e) What is the optimal consumption bundle (i.e. demanded bundle) if pg = $2, 19;, = $1 and m = $8? (f) What is the optimal consumption bundle if pa = $51 :01, = $1 and m = $4