Its a bunch of questions that need answering. The numbers that should be used to be substituted in is in the screenshot.
Microsoft Word - ECON203 problem set 2018.docx ECON203 problem set As part of your assessment in ECON203 you will be required to complete a set of technical problems that represent the theoretical/analytical component of the unit content. The rationale for this approach is to give you close-up experience with the way in which microeconomic arguments are represented technically through the use of models and simple mathematical techniques. Often this yields extra insights into the meaning of economic theory. The problem set is divided into three sections: A, B and C. The solutions for the Section A questions are due in Week 5. The solutions for Section B problems are due in Week 9. The solutions to the Section C problems are due in Week 13. The problem set will be released at the beginning of the unit, and the submission links will be live from the beginning of the unit as well. You can submit answers at any time. This means that you can submit Section A answers at any time until the deadline in Week 5, Section B answers at any time until the deadline in Week 9, and Section C answers at any time until the deadline in Week 13. Within those parameters the timing of your submission is completely up to you. The problem sets are personalised. Each student will have an individual set of numbers assigned to them. The problem set questions will require you to substitute values of particular numbers from your individual set for parameter values in the question. This means that every student will essentially have a different set of problems to complete. Although pooling of knowledge is desirable for improving understanding, keep in mind that a) the usual Academic Integrity requirements apply in relation to submitting only work that is entirely your own, and b) in some cases differing parameter values might cause your problem solutions to be qualitatively different from that of your peers. Problem solutions must be submitted in pdf form via the supplied links, preferably typed. If not typed then solutions must be completed in a highly legible form. Submissions written in hieroglyphics or alien languages, or in sizes suited to microfilm might not be marked. J Quite often the solution method to problems will be contained in worked examples in the textbook. Where not, suitable hints will be provided publicly. Some additional background information relating to mathematical methods will also be provided. Microsoft Word - Problem set.pdf GROUP A 1. An agent has a utility function over goods 1 and 2 of the form , where c is your individual number and d is your minimum number. The agent’s income is equal to your 2-digit number. The price of good 1 is your maximum number and the price of good 2 is your median number. Derive the agent’s demand functions for good 1 and good 2. Calculate the quantities of good 1 and good 2 in the agent’s optimum bundle. 2. An agent has a utility function over goods 1 and 2 of the form , where c is your 1- digit number and d is your minimum number. The agent’s income is equal to your 2-digit number. Initially, the price of good 1 is your median number and the price of good 2 is your individual number. Let the price of good 1 change to your maximum number. For good 1, determine for this price change the a) total price effect b) the substitution effect c) the income effect 3. For the same problem you analysed in Question 2, find for that price change the a) Laspeyres measure of the welfare change b) Paasche measure of the welfare change c) compensating variation d) equivalent variation GROUP B 4. a) Consider the problem you analysed in Question 2. Instead of the income value you used there, allow the agent to have an endowment of good 1 equal to the first digit of your 2- digit number, and an endowment of good 2 equal to the second digit of your 2-digit number. Derive expressions for the ordinary demands for both goods and calculate the gross and net demands for each good. b) An agent has a utility function over wealth given by where c is your 1-digit number. Their wealth if not robbed is equal to your 2-digit number multiplied by 1000. Should they be robbed, their wealth will be your maximum number multiplied by 1000. They assess the probability of being robbed as 1/(median number x 10). How much would this agent be prepared to pay for full insurance? How much would they have to pay for full (actuarially) fair insurance? 5. Consider the two agents, A and B. • Agent A has the utility function where c is your minimum number and d is your median number. A’s endowment of good 1 is the first digit of your 2-digit number, and A’s endowment of good 2 is the second digit of your 2-digit number. • Agent B has the utility function where e is your maximum number and f is your 1-digit number. B’s endowment of good 1 is the second digit of your 2-digit number, and B’s endowment of good 2 is the first digit of your 2-digit number. • The price of good 2 is your 1-digit number. a) Find the equilibrium price for good 1 and the gross and net demands of both agents for goods 1 and 2. b) Repeat the analysis for the cases where i. the values of c and d are swapped for A, and e and f are swapped for B. ii. the endowments of goods 1 and 2 are swapped for A, and the endowments of goods 1 and 2 are swapped for B [with c, d, e, f at their original – i.e part a) values]. 6. Consider the two agents, A and B. Each can choose one of two strategies, 1 and 2. The payoffs for the various outcomes are illustrated below (A’s payoffs listed first in each cell): Player B Player A where: • b is your individual number • c is your 1-digit number • e is your median number • f is the first digit of your 2-digit number • g is the second digit of your 2-digit number Strategy 1 Strategy 2 Strategy 1 3.5, b c, 2.5 Strategy 2 e, f g, 1.5 6.5, 5.5 3.5 a) Assume that A and B act simultaneously. Find all equilibrium strategy combinations of this game, including, where appropriate, mixed-strategy equilibria. Show A and B’s equilibrium payoffs. b) Rewrite this game in extensive form. Determine the equilibria and payoffs for the case in which A moves first, and the case in which B moves first. GROUP C 7. Consider a market in which all output is produced by two firms, A and B. The market inverse demand curve is given by where a is your two-digit number x 10 and b is your individual number. Both firms have a constant marginal cost equal to your median number. a) Find the Cournot equilibrium outputs for firms A and B, the equilibrium market price and the equilibrium profit for each firm. b) Repeat for i. the case where the marginal cost of firm B is constant and equal to your maximum number. ii. The case where there are n firms with marginal cost equal to your median number. Find the output of each firm, the market price and each firm’s profit, where n is the sum of your individual number and your median number. [Hint: with identical costs each firm’s output will be the same]. iii. The case where there are two firms A and B and the marginal cost for firm A is mAQA (where mA is your minimum number) and the marginal cost for firm B is mBQB (where mB is your 1-digit number). 8. Consider a market in which all output is produced by two firms, A and B. The market inverse demand curve is given by where a is your two-digit number x 10 and b is your individual number. Both firms have a constant marginal cost equal to your median number. a) Find the Stackelberg equilibrium outputs for firms A and B, the equilibrium market price and the equilibrium profit for each firm, on the assumption that firm A is the leader and firm B is the follower. b) Repeat for i. the case where the marginal cost of firm B is constant and equal to your maximum number. ii. The case where there are two firms A and B and the marginal cost for firm A is mAQA (where mA is your minimum number) and the marginal cost for firm B is mBQB (where mB is your 1-digit number). iii. The above two cases on the assumption that B is the leader and A the follower. 9. Consider a market a market for used cars in which cars can be either high-quality or low- quality. The demand for both types of car is perfectly elastic. The price buyers are willing to pay for a car known to be of low quality is your individual number x $2000 and the price they are willing to pay for a car known to be of high quality is your maximum number x $4000. Sellers are willing to accept a price equal to your minimum number x $1000 for a car known to be of low quality, and to accept a price equal to your median number x $3750 for a car known to be of high quality. The number of cars available for potential sale is equal to your 2-digit number x 200. The number of high-quality cars in that group is equal to your maximum number x 100. The supply of both cars is perfectly elastic up to the quantity of cars available. What will be the outcome in the market in terms of