Question

Suppose a young wine connoisseur enjoys two vintages in particular: a 2001 French Bordeaux (wf) and 2005 California varietal wine (). Her utility function is: Let Pc represent the price of the California wine and P represent the price of the french wine. Also let I be the income of the consumer In general, the combination of French wine and Californian wine that maximizes this consumers utility is w and w* Suppose the young connoisseur has $600 to spend to build a small wine cellar. Also suppose the price of the 2001 French Bordeaux (wf) is $40 per bottle while the less expensive 2005 California varietal wine (wc) is priced at $8 per bottle At the given prices and income, this consumer's utility maximizing combination of wine is wf - Suppose the young connoisseur has $600 to spend to build a small wine cellar. Also suppose the price of the 2001 French Bordeaux (wf) is decreases to $20 per bottle while the less expensive 2005 California varietal wine (Wc) is still priced at $8 per bottle At these new prices , this consumer's new utility maximizing combination of wine is w- and w* - - Before the change in prices, this consumers utility was approximately utility was approximately After the decrease in the price of french wine, this consumers Which of the following functions the consumers indirect utility function? 1/3 3P 3P 1/3 21 2/3 1/3 31 2/3 1/3 Plug in the new prices of wine Pf = 20, and Pc-8 into the indirect utility function V. Also plug in her level of utility achieved with the original prices (before the price decrease), into the indirect utility function for V. Finally, solve for I in the indirect utility function after plugging in these values. At the new prices of wine, this consumer would only need income equal to I~ with the original prices (without having extra income to purchase more wine and end up with a higher utility) in order to achieve just the same utility has she enjoyed

Answer 1

u(W_f, W_c) = W_f^2/3 W_c^1/3 P_f W_f + P_c W_c = I equation (1) optimal condition Mu_f/Mu_c = P_f/P_c Mu_W_f = (2/3)W_f^-1/3 W_c^1/3 Mu_W_c = (1/3)W_f^2/3 W_c^-2/3 (2/3)W_f^-1/3 W_c^1/3/(1/3)W_f^2/3 W_c^-2/3 = P_f/P_c 2W_c/W_f = P_f/P_c implies P_f W_f = 2P_c W_c (1) implies 2P_c W_c + P_c W_c = I W_c = I/3P_c W_f = 2P_c/P_f (I/3P_c) W_f = 2/3 I/P_f I = 600, P_w = 40 P_c = 8 W_c = 600/3(8) = 25 W_f = 2/3 (600/40) = 10 \r\n Now price decreases P_f = 20 P_c = 8 I = 600 W_f = 2/3 (600/20) = 20 W_c = 600/3(8) = 25 Before utility V_0 = (10)^2/3 (25)^1/3 = 13.57 equation (A) after utility V_1 = (20)^2/3 (25)^1/3 = 21.544 equation (B) consumer Indirect utility function option (d) implies V = (2/3 I/P_f)^2/3 (I/3P_c)^1/3 The last option is correct