d. b. 2 ; substitutes c. l ; complements d. 2 ; complements 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. b. c. d UDW> Suppose, initially, that I = 100 , Px = 2 and FY = 2. Graph this consumer's initial optimum point (A) in a. well-labeled graph. Your indifference curve should show whether strict convexity holds and whether it can hit an axis (or both). i. At these initial price and income levels, this consumer maximizes utility at by consuming units of X and units of Y. 1:50 2:49 l;49 2;50 The price of X falls to 1. Find the consumer's new optimum point (C) and label it on the same graph as in (e). Draw another indifference curve to show this new optimum. i. As a result of this fall in the price of X, this consumer now maximizes utility by consuming units of X and units of Y. a. 4 ;46 b. 2 ; 46 c. d. 2;48 4;4a 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. m: What do we know about good X for interior solutions here?] i. The equation of this consumer's initial, utility-maximizing indifference curve is: a. U) = 51 jollies b. U0 = so jollies 0 U0 = 49 jollies (1 U0 = 48 jollies Because for interior solutions, X is a(n) good, point B lies of point C. Inferior ; due West Normal ; due West Neuter ', due South Normal ; due South te: \"West\" and \"South" denote corn ass directions here. P iii. The coordinates of point B (substitution effect point) are: a. Xn=4;Yn=50 b. Xs=4;Yu=47 c. Xa=l;Ya=48 d. Xa=l;YB=47 1,, , .m. _. _.: ._.-_t.i .. ...:|:... ._....:...:-m mm. nub-rt" mmuav auroral-mp: has n 9:52 Done 301PS2F21.pdf 2. A utility maximizing consumer has the following utility function: U(X, Y) = 2X12 + Y a. Are these preferences strictly monotonic? Strictly convex? Explain. i. The preferences represented by this utility function are monotonic and convex. a Weakly ; weakly b . 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 b . ( PY / Px )2 ; I/ Px ; 0 C. Px / Py ; Py/ Px ; I/ PY d. ( PY )2 / Px ; ( PY/ Px ); (I/PY) - ( Py/ Px ) ii. If I is less than or equal to then the optimum is a corner solution, and he buys Px / Py ; all X and no Y. ( Py / Px )2; all Y and no X. ( Py )2 / Px ; all X and no Y. ( PY )2 / 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: -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