hi there, I sent you the actual requirements for the assignment and 2 examples for it!
Ryerson University Department of Economics CECN230 Mathematics for Economics Angelique Bernabe Spring 2021 Real Life Example Assignment This project requires you to apply the course material to formulate and solve an economic problem. You can choose any topic from 1 to 8. Instead of the prof and the textbook authors trying to dream up a real-life example, you have to dream up a real life example. Similarly to the prof or textbook examples, your “real life” example does not have to be perfectly realistic. For example, in real life you may buy more than two items at a grocery store. But in your example, there will just be two goods or two items, etc. Use our existing theoretical tools – for example, Cobb Douglas (production function), or Linear preferences. You do not have to dream up a new, more realistic kind of preferences but use the tools from the course. The project should be ONE PAGE long. It should be typed, not hand written. You will need to use an Equation editor (available in Microsoft Word) or make extensive use of symbols (also available in Microsoft Word) in your word processor. Explain the real life situation you are trying to illustrate. Show your equations and explain each variable used. Explain why the equations (e.g. Cobb Douglas utility function), tools (e.g. Derivatives, elasticity, linear algebra) and variables (e.g. Labour, capital) you have chosen are appropriate. Solve the real life situation according to the techniques learned in CECN230, to find some answer you are interested in. Show ALL your steps. Comment on the answer you obtained. Bonus: Educational Memes Contest Using the course content, you have to create an educational meme. For more infor- mation about memes, please visit this page. 1 https://en.wikipedia.org/wiki/Internet_meme Grading Criteria - Creativity (2.5 points) - Credibility (2.5 points) - Math clarity (2.5 points) - Math errors (2.5 points) 2 Ryerson University Department of Economics CECN230 Mathematics for Economics Angelique Bernabe Spring 2021 Real Life Example Assignment - Example: Student Budget Students normally live on a fairly tight budget. Students have low income while having to pay for housing, food, tuition, etc. In this assignment, I therefore want to analyze the budgeting decisions of students (in this section: provide more context and why this is important). For simplicity, I assume that students only have two goods to choose from. The student must consume housing and brunch and the budget must break-even. I assume that the cost of housing is $100 square meter and the student can choose how big this apartment is. Brunch in Toronto cost $25 per brunch (in this section explain the assumption you are making and why you are making them). The student has to consume both housing and brunch, I assume the following utility function: U(B,R) = B ∗R where B is brunch and R is the rent. I choose those exponents so that (explain why; randomly is not an explanation). In addition, I know that the minumun wage in Ontario is $14 per hour and I know that a student will work a maximum of 15 hours per week in order to maximize their study time. If I assume that a student makes $3 above minimum wage, then this implies that a student can work 60 hours a month at $17 which leads to a budget of $1020. The student wants to maximize their utility subject to their budget constraint: max(B ∗R) s.t 25B + 100H = 1020 1 Isolating the budget for B, I get: B = 40.8−4R which I then plug into my optimization problem: (40.8− 4R)R (In this section, show how you get to the answer; F.O.C.s, etc.) After taking the F.O.C.s and solving for both the number of brunch and the size of the apartment. I get that student will demand 5.1 square meter apartment and 20.4 brunches per month (in this section, explain how this makes sense and how it helps understand the question you wanted to analyse in this assignment). 2 Ben Armishaw 501005389 August 10, 2020 CECN230 Mathematics for Economics Real Life Example Assignment: Award Winning Actresses Just two weeks ago the nominations for the 2020 Primetime Emmy’s were released. Among the nominees was Olivia Colman, for her performance in The Crown. If she were to win this award she would join a small list of actresses who have won the three biggest acting awards, which are the Tony, the Oscar, and the Emmy. Olivia Colman has requested that her agent figure out the value each one of these major acting awards would add to her compensation for the next film she is making. Her agent has decided that the best way to find the value of each award, would be to look at actresses in a similar age range who have won all three awards and see what the market paid them for their last feature film. Frances McDormand has one Tony, two Oscar’s, and one Emmy and was paid $10 million for her last film. 1t+2o+1e=10 T = # of Tony’s. O = # of Oscar’s. E = # of Emmy’s. Viola Davis has two Tony’s, one Oscar, and one Emmy and was paid $8 million for her last film. Which would translate to the following equation: 2t+1o+1e=8 Helen Mirren has one Tony, one Oscar, and four Emmy’s and was paid $9 million for her last film. 1t+1o+4e=9 The equations derived from the actresses now have created a system of equations, which is as follows: 1t+2o+1e=10 2t+1o+1e=8 1t+1o+4e=9 Angelique Bernabe Angelique Bernabe Which then translates into the following matrix: 1 2 1 10 2 1 1 8 1 1 4 9 Using Gaussian elimination, we are able to isolate and solve for the variables by combining the different rows. 1 2 1 10 1 2 1 10 1 2 1 10 2 1 1 8 0 -3 -1 -12 0 -3 -1 -12 1 1 4 9 1 1 4 9 0 -1 3 -1 1 2 1 10 1 2 1 10 1 0 7 8 0 -1 3 -1 0 1 -3 1 0 1 -3 1 0 -3 -1 -12 0 -3 -1 -12 0 -3 -1 -12 1 0 7 8 1 0 7 8 1 0 0 17/10 0 1 -3 1 0 1 -3 1 0 1 0 37/10 0 0 -10 -9 0 0 1 9/10 0 0 1 9/10 T=1.7 Million O=3.7 Million E=.9 Million Through Gaussian elimination Olivia Colman’s agent was able to find out that a Tony is worth $1.7 million, an Oscar is worth $3.7 million, and an Emmy is worth $.9 million. So, if Oliva Colman is able to win the Emmy this September, she will have one won of each award which would mean her salary for her next film would be $6.3 million.