please answer all of them. thank you.

1. (36 points) Two firms, A and B, are competing in the production of a homogenous good. The good's marginal cost for both firms is equal, MC = $25. Assuming linear reaction functions, describe what would happen to output and price in each of the following situations if the firms are in (i) collusive equilibrium, (ii) Cournot equilibrium, (iii) Bertrand equilibrium. (a) (4 points for each of (i)-(iii)) The demand curve shifts to the left. (b) (4 points for each of (i)-(iii)) Because it invents a new and improved machine, the marginal cost at firm B decreases to $20. (c) (4 points for each of (i)-(iii)) Costs in the entire industry increase due to an increase in wages.3. (28 points) Suppose a perfectly competitive labor market has a demand curve of LP = 120 - 2w and a supply curve of L' = 8w, where w is the wage rate is dollars and L is the quantity of labor in person-hours. (a) (2 points) What are the equilibrium values of the wage and employment? (b) (4 points) Suppose the government imposed a minimum wage of $14 per hour. Now what are the equilibrium values of the wage and employment? (c) (8 points) Repeat part (a), assuming now that the market is a monopsony. (d) (8 points) Repeat part (b), assuming now that the market is a monopsony. (e) (6 points) Does the imposition of the minimum wage decrease employment here under perfect competition? What about under monopsony? Give a brief intuitive explanation for your answer and why it may be different under the two different market structures.4. (11 points) Suppose you face the following lottery. You can earn 1 of 3 possible grades in this class: an "A", a "C", or an "F", with the following probabilities: TA= 2 6 2 10 TO = 10 10 Your current wealth (w) is $400. If you receive an "A", you gain (e.g. I pay you) $500. However, if you get an "F", you lose (e.g. you pay me) $300. If you receive a "C", you DO NOT GAIN OR LOSE anything. Assume your utility function, defined over wealth, is U(w) = (w). (a) (6 points) What is your expected utility (EU)? [Hint: be sure to calculate your total wealth in each "state". ] (b) (5 points) What is the certainty equivalent level of wealth (w*), that is, the guaranteed payoff at which a person is "indifferent" between accepting the guaranteed payoff and their expected utility from (a)?1. (25 points) For each of the following scenarios, use a supply and demand diagram to illustrate the effect of the given shock on the equilibrium price and quantity in the specified competitive market. Explain whether there is a shift in the demand curve, the supply curve, or neither. (a) (5 points) An unexpected temporary heat wave hits the East Coast. Show the effect in the ice cream market in New England. (b) (5 points) The government introduces a tax on ice cream which is paid by producers. What is the effect in the ice cream market? (c) (5 points) China and Mexico are major producers of textiles. Workers in Mexico decide to go on strike. Show the effect on the market for Mexican textiles. (d) (5 points) Show the effect of the situation described in (c) on the market for Chinese textiles. (e) (5 points) Suppose the government imposes a price cap on bottled water. Show the effect in the bottled water market.2. (20 points) For each of the following pairs of goods, identify which one you would expect to have more own-price elastic demand. Please explain your reasoning. (a) (5 points) Computers (generally) vs. Apple MacBook Pro laptops. (b) (5 points) Stereo headphones (generally) vs. hearing aids. For each of the following goods, identify whether you would expect demand to be more (own-price) elastic in the short run or the long run. As above, please briefly explain your reasoning. (c) (5 points) Retail gasoline in the suburbs of Chicago. (d) (5 points) Air conditioning units in Miami Beach, Florida.3. (30 points) Consider the market for apple juice. In this market, the supply curve is given by Qs = 10PJ - 5PA and the demand curve is given by QD = 100 - 15PJ + 10Pr, where J denotes apple juice, A denotes apples, and T denotes tea. (a) (7 points) Assume that PA is fixed at $1 and Pr = 5. Calculate the equilibrium price and quantity in the apple juice market. (b) (7 points) Suppose that a poor harvest season raises the price of apples to PA = 2. Find the new equilibrium price and quantity of apple juice. Draw a graph to illustrate your answer. (c) (8 points) Suppose PA = 1 but the price of tea drops to Pr = 3. Find the new equilibrium price and quantity of apple juice. (d) (8 points) Suppose PA = 1, Pr = 5, and there is a price ceiling on apple juice of P} = 5. What is the excess demand for apple juice as a result? Draw a graph to illustrate your answer.4. (25 points) You have been asked to analyze the market for steel. From public sources, you are able to find that last year's price for steel was $20 per ton. At this price, 100 million tons were sold on the world market. From trade association data you are able to obtain estimates for the own price elasticities of demand and supply on the world markets as -0.25 for demand and 0.5 for supply. Assume that steel has linear demand and supply curves throughout. (a) (10 points) Solve for the equations of demand and supply in this market and sketch the demand and supply curves. (b) (15 points) Suppose that you discover that the current price of steel is $15 per ton and the current level of worldwide sales of steel is 150 million tons. The most recent elasticity estimates from the trade association this year are -0.125 for demand and 0.25 for supply. Describe the change in the supply and demand curves over the past year using your diagram from part (a). What sort of event (s) might explain the change?1. (10 points) Annie and David are painting their apartment. At the paint store, David says he prefers Canary Yellow to Bumblebee Yellow, Lime Yellow, and Crayola Yellow. Annie finds new paint samples and asks David to compare Canary Yellow to School Bus Yellow and to Sunrise Yellow. David prefers Sunrise Yellow to Canary Yellow, and prefers School Bus Yellow to Canary Yellow. He also prefers Sunrise Yellow to School Bus Yellow. The store is out of Sunrise Yellow, so they buy School Bus Yellow and paint their apartment with it. David then insists that they go back, buy Lime Yellow, and repaint the apartment. True/False/Uncertain: David has rational preferences (as we define them).2. (20 points) In each of the following examples, a consumer purchases just two goods: r and y. Based on the information in each of the following parts, sketch a plausible set of indifference curves (that is, draw at least two curves on a set of labeled axes, and indicate the direction of higher utility). Also, write down a utility function u(x, y) consistent with your graph. Note that although all these preferences should be assumed to be complete and transitive (as required for utility representation), not all will be monotone. (a) (4 points) Jessica enjoys bagels r and coffee y, and consuming more of one makes consuming the other more enjoyable. (b) (4 points) Plamen loves mocha swirl ice cream a, but he hates mushrooms y. (c) (4 points) Jennifer likes Cheerios a, and neither likes nor dislikes Frosted Flakes y. (d) (4 points) Edward always buys three white tank tops a for every pair of jeans y. (e) (4 points) Nancy likes both peanut butter ar and jelly y, and always gets the same additional satisfaction from an ounce of peanut butter as she does from two ounces of jelly.3. (20 points) A consumer's preferences are representable by the following utility function: u(x, y) = x ty. (a) (10 points) Obtain the MRS of the consumer at an arbitrary point (x, y), where i > 0 and y > 0. (b) (10 points) Suppose the price of the second good (y) is 1, and the price of the first good (z) is denoted by p > 0. If the consumer's income is m > 0, obtain the optimal consumption bundle of the consumer (in terms of m and p). [Caution: make sure you cover cases in which m is relatively low, as well as cases in which m is relatively high.]4. (25 points) It is exactly 24 hours before Lauren's physics final. She has an economics final directly after the physics final and has no time to study in between. Lauren wants to be a physicist, so she places more weight on her physics test score. Her utility function is given by u(p, e) = 0.6 In(p) + 0.4 In(e) where p is the score on the physics final and e is the score on the economics final. Although she cares more about physics, she is better at economics; for each hour spent studying economics she will increase her score by 3 points, but her physics score will only increase by 2 points for every hour spent studying physics. Studying zero hours results in a score of zero on both subjects (although In(0) is not defined, assume her utility for a score of zero is negative infinity). (a) (5 points) What constraints does Lauren face in her test score maximization problem? (b) (5 points) How many hours should Lauren optimally spend studying physics? How many hours studying economics? (hours are divisible) (c) (5 points) What economics and physics test scores will she achieve (i.e. what are e" and p")? (d) (5 points) What utility level will she achieve? (e) (5 points) Suppose Lauren can get an economics tutor. If she goes to the tutor, she will increase her economics test score by 5 points for every hour spent studying instead of 3 points, but will lose 4 hours of study time by going to the tutor. She cannot study while at the tutor, and going to the tutor does not directly improve her test score. Should Lauren go to the tutor