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Econ 250, Spring 2021 Midterm 1 Professor Diana Ngo Name: Please copy and sign the following statement below your name. I confirm that the entirety of my completed exam is my own work, done without any consultation with classmates or other individuals. Instructions. Please read carefully. • The exam is worth 100 points. • Be safe: If you start your exam and some connectivity or other issue occurs (e.g., your internet goes down), stay calm and continue to stay where you are. Contact me as soon as you are able, and we will work together to figure out a solution. • Deadline: The midterm is due by 12 noon on Friday, 2/19. Please upload it on the Moodle Dropbox, similar to your assignments. There will be a 5 point penalty if you hand it in between 15 and 30 minutes late, and an additional 5 point penalty for every half hour late thereafter. • Questions during exam: If you have questions during the exam, you may email me. As I would in person, I will clarify if possible or tell you that I cannot answer the question if it is something you are being tested on. • Individual exam: This exam is to be completed individually – you may not consult with any classmates or other people. • Other resources: This is an open-book exam, so you may use any resources (except for other people) available to you, including the textbook, lecture notes, homeworks, calculators, and the internet. • Format: You may print out this exam and complete it on the exam sheet, or you can write your solutions up on blank pieces of paper (like your homework). • Graphical problems: Some of the solutions depend on accurate graphing of certain curves/points, so please carefully label all of your axes with numbers and label important points with their coordi- nates. • Partial credit: Show work whenever possible, provide detailed steps of how you would solve a problem if you cannot solve the math, and clearly identify your solution. To the best of your ability, please try to answer all parts of all questions. Recall that there is partial credit for information that is relevant to the question. If you are unable to answer the first part of a question, you should make up a solution if it is necessary for the second part and answer accordingly. • Try your best: That’s all that we ask for. And know that we all recognize that you are doing what you can conditional on these exceptionally challenging times. 1 For grading purposes only Question Points 1 2 3 4 5 6 Final score 2 Note: For the graphical problems, the solution depends on accurate graphing/numbers, so please clearly mark off your axes and label the important points on your curves. That is, if you want me to look at points (3,1) and (2,5), you should clearly mark them and label them with numbers. If you are not writing on this paper, you should reproduce the graphs with the axes as labeled (e.g., make sure your horizontal good matches the horizontal good given.) 1. (10 points) Eloise and Penelope have preferences over ballgowns (B) and journals (J) for capturing gossip and unpacking mysteries. Eloise’s utility function is given by: UEloise(B, J) = 2 lnB + ln J Penelope’s utility function is given by: UPenelope(B, J) = B 2 3J 1 3 TRUE OR FALSE: It is possible that they have the exact same preferences for all positive values of B and J . Demonstrate using math and graphs, and explain (2 sentences maximum). 3 2. (18 points) The people of Shondaland buy scandals, S, and more wholesome entertainment, E. Each person has $100 to spend on them, and the prices are originally $5 for scandals and $10 for entertainment. On a whim, Lady Whistledown offers a deal where she promises that everyone will have a minimum of 4 scandals (that is, if they purchase less than 4 scandals, she will freely offer scandals so they end up with at least 4 scandals). In addition, if they purchase 12 or more scandals, she will give them $40 in cash that they can spend on either good. (a) (9 points) Plot the budget constraints with and without the deal. No explanation is necessary. (b) (9 points) Daphne’s utility function for scandals and entertainment is given by U(S,E) = √ 3S + βE where β is an unknown number. She faces the same income and deal as everyone else. If possible, determine the range of values for β that make it optimal for her to choose 12 scandals after the deal. If it is not possible, explain why not. 4 3. (18 points) The people of London have a standard hourly wage represented by the budget constraint, BCstandard, in gray. In a spark of generosity, Queen Charlotte introduces a program represented by BCprogram, in black. (a) (9 points) Describe the pay deal represented by BCprogram. You should use specific numbers. (5 sentences max). 5 (b) (9 points) Provide an analysis of the different potential effects of the program using the graphs below. You need not use all the graphs, or you may add additional graphs if necessary, but you should provide a comprehensive description of the potential effects. You should describe the results for each scenario that you depict. Assume that people’s preferences are smooth and curved and do not violate any assumptions. You do not need to refer to specific numbers. 6 4. (18 points) Anthony spends all his money on whiskey, W , and operas, O. His income is 24. The price of operas is 1. His utility is U(W,O) = W 2 3O 1 3 The price of whiskey was 16 initially and then decreased to 2. Whiskey is a normal good. (a) (9 points) Draw a graph with budget constraints and indifference curves, identifying the total effect, income effect, and substitution effect for WHISKEY consistent with the description. Label the relevant curves using the subscript 1 to indicate before the price change and the subscript 2 to indicate after the price change. Label the optimal consumption bundles before and after the price change as A and B, respectively. Full credit will be given for a graph where the total effect, income effect, and substitution effects are in the correct directions, even if the magnitudes are not precise. 7 (b) (9 points) Calculate the exact size of the income effect for WHISKEY. 8 5. (18 points) Lord Featherington’s utility function over betting (B) and fighting matches (M) is given by U(B,M) = √ B + 3M His income is given by I. The price of betting is PB, and the price of matches is PM . (a) (9 points) Determine the formula for his DEMAND curve for BETTING. (b) (9 points) Determine the income elasticity of his demand for BETTING for all positive values of income. Determine whether or not BETTING is a normal good, an inferior good, or neither, and explain why. (2 sentences maximum.) 9 6. (18 points) In Hastings, inverse demand and supply for hogs is given as below. Inverse Demand: P = 1100− 1 3 Q Supply: Q = 100 + 5P To make up for his social blunder, Simon institutes an S dollar unit subsidy on hogs. (a) (9 points) How does the post-subsidy equilibrium quantity change given a small increase in the size of the subsidy? Provide the calculation and interpret. (b) (9 points) How does the share of the subsidy received by the producers change given a small increase in the size of the subsidy? Provide the calculation and interpret. Show all your work (including the original formulas and steps before and after simplification). 10