deriving function; microecon 100

general equalibrium; optimal choice

1.) Stacey needs two packs of sweetener for every cup of coffee. Derive the demand function for perfect 2-1 complements, u(X1, X2) = min {2x1, x2} 2.) John does not care whether he drinks two 8 ounce sodas or one 16 ounce soda. Derive the demand function for perfect 2-1 substitutes, u(X1, X2) = 2x1 + X2. 3.) Laura has preferences over money and all other goods. Derive the demand func- tion for quasilinear preferences, u(1, X2) = X1 + In(x2). 4.) Doug's preferences are given by u(1, X2). Which transformations of his utility function below represent the same preferences? (a) 2u(x1, 2) - 1000 (b) -2u(21, 2) + 1000 (c) u (21 , 12 ) (d) 40 u(x1,X2) 5.) Consider the following allocation (xA, xA) = (1, 1) for Albert and (X3, X3) = (3, 3) for Berta. Under which of the preferences below is this allocation Pareto efficient? (a) uA = xA and UB = T'3 (b) uA = xA + xA and UB = XB + XB (c) WA = (24)1/3 . (x2)2/3 and UB = (23)2/3 . (13) 1/3 (d) uA = xA . x2 and UB = TB . IB