ENGM90011 Tutorial 1 1. If you see one movie per week, how many movies do you see on average in a month? 2. Consumption Sets X. For each of the following, draw the consumption set X. (Assume two goods and remember quantities are assumed to be non-negative real numbers). a. Good 1, C, is litres of ice-cream per day and good 2, Z, is hours of leisure time per day. b. Same as part a), but government regulations forbid working more than 16 hours per day. c. Good 1, M, is litres of ice-cream today in Melbourne and good 2, S, is litres of icecream today in Sydney, and you can only be in one city today. 3. On the last slide of the Consumer Choice 1 lecture notes, we drew indifference curves when movies were good and pizzas were bad. Keeping movies on the horizontal axis and pizzas on the vertical axis, will there be any difference in the indifference curves if movies were bad and pizzas were good? 4. Tom likes water but cares only about the total amount of water. Water comes in two sizes: 250 ml and 500 ml bottles of water. Define a bundle to be (number of 250mL bottles, number of 500mL bottles). a. Putting the number of 250 ml bottle on the x-axis and the number of 500 ml bottle on the y-axis, draw three of Tom’s indifference curves representing bundles with that are equally ranked (indifferent) to bundles (1, 1), (2, 2), and (3,3) respectively. b. Do Tom’s preferences satisfy monotonicity? Do Tom’s preferences satisfy strong monotonicity? 5. Let a bundle be a pair of non-negative real numbers (n1, n2). Max’s preferences over the bundles are as follows: For any two bundles, Max prefers the bundle that has the largest number (of the four numbers from the two bundles). Max is indifferent between the two bundles If both bundles have the largest number. a. Draw Max’s indifference curves corresponding to bundles (n1, n2) = (2, 2), (2, 3) and (3, 4) respectively. b. Do Max’s preferences satisfy monotonicity? Do Max’s preferences satisfy strong monotonicity? ENGM90011 Tutorial 1 6. There are two goods: gin (g) and tonic water (t), (measured in cups say). Let 𝒙 = (𝑔, 𝑡), 𝒙′ = (𝑔′ , 𝑡′) ∈ 𝑿. Minnie’s preferences over bundles of gin and tonic are as follows: If 𝑚𝑖𝑛(2𝑔, 𝑡) > 𝑚𝑖𝑛(2𝑔′, 𝑡′) then 𝒙 ≻ 𝒙′. If 𝑚𝑖𝑛(2𝑔, 𝑡) = 𝑚𝑖𝑛(2𝑔′, 𝑡′) then 𝒙 ~ 𝒙′. a. Draw Minnie’s indifference curves corresponding to bundles (g, t) = (2, 2), (2, 3) and (2, 4) respectively. b. Do Minnie’s preferences satisfy monotonicity? Do Minnie’s preferences satisfy strong monotonicity? 7. Let there be two goods: movies and pizzas. Define a bundle to be (number of movies, number of pizzas). Sadie’s preferences for movies and pizzas can be explained by two facts: i. All bundles an equal distance from (30, 50) are indifferent to each other. ii. Bundles further away from (30, 50) are less preferred than bundles closer to (30, 50). a. Draw some of Sadie’s indifference curves. b. Do Sadie’s preferences satisfy monotonicity? 8. There are two goods x and y. Milton preferences for bundles of x and y can be described as follows: Between any two bundles, Milton prefers the bundle that has more x. If two bundles have the same amount of x, he prefers the bundle that has more y. (Obviously, bundles with the same amount of x and y are the same bundle). a. Prove that Milton’s preferences satisfy the completeness assumption. b. Describe what the indifference curves look like. ENGM90011 Tutorial 1