Question

Erin has the following utility over cookies and leisure. U = min(31,c) (Utility) 5 € 4 3 2 1 0 0 0.33 0.67 + 5 1 2 3 4 Her indifference curves are plotted in the above graph. She can choose from the following five bundles for leisure and consumption (l,c): 1. Point 1: (3,3) 2. Point 2: (2,2) 3. Point 3: (1,1) 4. Point 4: (3,2) 5. Point 5: (3,1) a. What is her utility from each bundle? b. Reproduce the graph above and label each of the 5 bundles on the graph. c. Assume that Erin can just pick a bundle without having to pay anything for it. Which bundle(s) will Erin choose? Now, suppose Erin has a budget constraint given by W(T-1) = pc where w = 6, p=1, T = 3. 2 d. Suppose Erin must pay for any bundles she chooses. Can she afford the bundle(s) she would have picked in c.? Explain why or why not. e. Suppose Erin chooses consumption and leisure to maximize her utility given the budget constraint and parameters for w,p, T specified above. Then, Erin's wage increases. Will she choose more leisure than before? Explain why or why not.

Answer 1

Point (3,3) utility: u min{ 1, Jo min{9,3} = 3 Point 2: (2, 2) utility: u min{31, c} = minęs, az = 2 Point 3: (1, 1) ubility: " min{31, c} = Frinſ, i} pointa : (3, 2) utility: u= min! min {3d, c} = 2 point 5 : (3, 1) utility: mina, u= b 5 xe 4 3 2 2 3 5 1 0 0 0.33 0.67 1 2 3 4 5 one she will bundle chose If she can chose any that will give her maximum utility Then she will chose point utility ; u = 3. (3,3) with d. Budget: 6(3-1) = c. Ct3L = 18 At (l,c) → (3,3) c + 3 l 12 < 18 Therefore she can chose the bundle afford the bundle She chose at Ce). e. At equilibrium: 34C ..38 + 3/18 :. e*. 3, If wage mises ; budget: W(T-1) þct wl with 3-C 5 WT pt wo) 1 WT WT 3ptu al aw Now 3 T (3p+w)2 >0 as W mises l mises.