Homework answers / question archive / Alice has perfect—complement preferences, with , a: uA(a:1,a:2) = mm{§1,x2} Her income is y : 60 and prices are p1 : 6,132 = 2

Alice has perfect—complement preferences, with , a: uA(a:1,a:2) = mm{§1,x2} Her income is y : 60 and prices are p1 : 6,132 = 2

Economics

Share With

Alice has perfect—complement preferences, with , a: uA(a:1,a:2) = mm{§1,x2} Her income is y : 60 and prices are p1 : 6,132 = 2. The point of this exercise is to calculate the substitution and income effects of a change in prices on Alice’s demands. You can review Notes 8 to help interpret these calculations.

(a) Find Alice’s demands for each good, with y = 60, p1 = 6,192 = 2. Call her demands (3:1, 3:2). Draw a diagram showing the budget line and the indifference curve through her choice. (b) Suppose p1 is decreased to 191 = 4, with y and p2 unchanged. Find the new demands, and draw a new diagram. Call the new demands (101,102).

(C) Now we want to isolate the substitution effect of this change in price. First, ?nd the equation for the budget line going through Alice’s choice from part (2a), but with the slope determined by the prices in part (2b). That is, the budget line if Alice were endowed with her old choice at the new prices. (This is the red line in Slide 6 of Notes 8.) Find Alice’s choice given this budget line, and call it (21, 22). State the substitution effect for each good, i.e. how much more does she consume of each good compared to part (2a)? This is zl — x1 and 22 — 352. If she consumes less of a good, that answer will be negative. After the substitution effect alone, ?nd Alice’s new utility. Is it higher, lower or equal to her utility from the choice in (a)? Answer numerically, but also explain why the answer must be this way. Now ?nd the income effect on each good. The income effect comes from the budget line in part (10) changing to that in part (2b), and Alice changing her choices accordingly. That is, the income effects are 101 — 21 and 102 — 22.