ECO 420K Spring 2023Assignment 2 Due: Sun, Jan 29, by 11:59pmDelivery: Upload to Canvas as a single file.Note: Assignments submitted as a single file will receive 2 bonus points.Problem 1. [15...

Attached


ECO 420K Spring 2023 Assignment 2 Due: Sun, Jan 29, by 11:59pm Delivery: Upload to Canvas as a single file. Note: Assignments submitted as a single file will receive 2 bonus points. Problem 1. [15 points] Consider a scenario with two goods. a. Draw an indifference curve that represents convex preferences. On another graph, draw an indifference curve that represents concave preferences. b. In each of your graphs, identify roughly where the marginal rate of substitution (MRS) is less than −1, equal to −1, and greater than −1. c. Interpret the MRS in each of these regions. In other words, what does it mean when MRS < −1,="" mrs="−1," and="" mrs=""> −1? d. For each curve, briefly describe what happens as x1 (the good on the x-axis) increases and traverses each region you identified in (b). Problem 2. [15 points] You just graduated with a degree in economics and have three job offers across the country. You are not sure which job to accept, but you care about salary and being close to nature. The three jobs can be summarized as follows: • Job A pays a high salary but has no natural attractions nearby. • Job B pays a low salary but, nearby, there are spectacular mountains and beaches. • Job C has a medium salary and some nice hiking trails nearby (but nothing special). Suppose you are indifferent to jobs A and B and assume the jobs can be plotted as follows (where the dotted line is simply a visual aid): a. In terms of your preference for job C compared to jobs A and B, what would make your preferences concave? What about convex? 1 ECO 420K Spring 2023 b. What would make location and salary be perfect substitutes for you? c. Do you think it makes sense to think of salary and location as perfect substitutes? Why? Problem 3. [15 points] Suppose commodity 1 is a good until the quantity x∗1, after which it becomes a bad. In other words, x∗1 is the perfect amount of commodity 1. Suppose that you can’t get enough of commodity 2. That is, commodity 2 is always a good. a. Draw an indifference curve for this scenario and clearly label x∗1 on your graph. b. Why does it look like this? Briefly explain. Problem 4. [25 points] Josh’s utility function for goods 1 and 2 is given as: u(x1, x2) = 2x 2 1x2 Josh has a budget of $m to spend on goods 1 and 2. Assume that the price of good 2 is 3 times the price of good 1. In other words, p2 = 3p1. a. State the optimization problem for Josh, including the constraints. b. Do you think the solution will be an interior or a corner solution? Explain. c. Solve for Josh’s optimal consumption choice (x∗1, x ∗ 2). Note: Your answer should be expressed in terms of m and p1 only. Problem 5. [30 points] Helena is going to dinner at the local Latin American restaurant in Austin. She can’t wait to have fresh fruit juice (j) and appetizers (a). Her preferences can be represented by the following utility function: U(j, a) = 2 ln(j) + 3 ln(a) a. Compute the marginal rate of substitution of juice for appetizers. Is the MRS increas- ing or decreasing in j? Briefly interpret this. b. Suppose the price for juice is pj = $2 and the price of each appetizer is pa = $5. Suppose that Helena’s budget for dinner is $25. What should Helena order for dinner in order to maximize her utility? c. Suppose the price of juice increases to pj = $4. What should Helena’s new order be? d. Given the price increase, by how much would Helena have to increase her dinner budget in order to obtain the same utility as was possible before the price change? e. What would Helena order for dinner with her higher dinner budget, given the price increase? 2