b. Derive an expression for this consumer's income consumption curve. Derive an expression for this consumer's price consumption curve for PX . Comment on their similaIities or differences. i. This consumer's income consumption curve is: a. Y* = X\" I). Y* = 2 X* c. Y* = '/2X* (1. Y* = 3:2 X* ii. This consumer's price consumption curve for P): is: a. Y* = X\" 13. Y* = 2 X\" c. Y\" = 1/5 X" d. Y" = 312 X* iii. This consumer's price consumption curve for P): and their income consumption curve are , because any change in P): results in ili. This consumer's price consumption curve for Px and their income consumption curve are , because any change in Px results in a. Different ; a stronger substitution effect than income effect Different ; no income effect The same ; a stronger substitution effect than income effect d. The same ; no substitution effect 2. A utility maximizing consumer has the following utility function: U (X, Y) = 2X12 + Y a. Are these preferences strictly monotonic? Strictly convex? Explain. 1. The preferences represented by this utility function are monotonic and convex. a. Weakly ; weakly Weakly ; strictly Strictly ; weakly Strictly ; strictly b. Assuming our utility maximizer faces a linear budget constraint of the form PxX + PyY = I , derive his/her optimal demands X*( Px , Py , I ) and Y*( Px , Py , I ) . You may use any method you prefer, but please show your work. If these demands are piecewise functions, then state each piece clearly (namely, is a corner solution possible, and, if so, what would X* and Y* be then?) i. If I > , then this consumer's optimal demand for X is and his optimal demand for Y is a. Px / Py ; I / Px ; 0 (Py/ Px ) ; I / Px ; 0 C. Px / Py ; Py/ Px ; I /PY d. ( PY )? / Px ; (Py/ Px) ; (1/Py ) - (Pv/Px )ii. If I is less than or equal to then the optimum is a corner solution, and he buys a. Px / Py ; all X and no Y. ( Py / Px )' ; all Y and no X. ( PY )' / Px ; all X and no Y. ( Py )' / Px ; all Y and no X. C. Assuming an interior optimum, what is the own-price elasticity of demand for X? The cross price elasticity of demand for X with respect to Py? i. At any interior optimum here, the own-price elasticity of demand for X is: a. b. C. -2 d. -1/2 ii. At any interior optimum here, the cross-price elasticity of the demand for X with respect to Py is implying that X and Y are a. 1 ; substitutes b . 2 ; substitutes C. 1 ; complements 2 ; complements d. Graph the Engel curve for Y. Label intercept and slope values carefully. i. Which of the following graphs (located at the end of these questions!) correctly depicts the Engel curve for Y? a. C.Suppose, initially. that I = 100 , Px- 2 and P7 = 2. Gmphthis consumer's initial optimum point {A} in a well-labeled graph. Your indifference curve should show whether strict convexity holds and whher it can hit an axis (or both), i. At these initial price and income levels, this consumer maximizes utility at by consuming units ofX and waits on. a. l ; 50 b. 2 : 49 c. 1 ; 49 d. 2 1 50 The price of K falls to 1. Find the consumer's new optimmri point (C) and label it on the same graph as in (e), Draw another indifference move to show this new optimum. i. As a result of this fall in the price of X. du's consumer now maximizes utility by consuming units of X and units on. a. 4 ; 46 b. 2 ; 46 c. 2 ; 48 :1 4 ;43 Find the coordinates of the substitution effect point (B) of this price change. Label it and draw the compensated budget line tangent to the original indifference curve through point A. Mm: What do we know about good X for interior solutions here?] i, The equation of this consiuner's initial, utility-madmizing indifference curve is; a. Un I 51 jellies b. U0 = SDjollies c. Uo = 49 jellies d. U} = 43 jellies ii. Because for interior solutions. X is 1101) good, point B lies of point C. a. Inferior ; due West b. Normal; due West c. Neuter ; due South d Normal ; clue South M: \"West" and \"South\" denote compass directions hem]