Submission details: A complete submission should contain: (1) A function of your choosing. (a) The function should be named by the capitalized first letter of your last name and variable names should be the consonants of your first name. For example, for me the function would be 30:, r). (b) The function should be a function of at least two variables and should contain at least two parts of different nature. For example, one part can be a polynomial, another part an exponential function. Parts could also be rational functions or logarithms. (2) Describe the level curve through the point (2, 5). (3) Compute all first partial derivatives of your function. (4) Compute the partial elasticity with regard to the variables that your function depends on. (5) Find a linear approximation to your function in the proximity of point (1,1). (6) Consider the level curve you described in (2). It implicitly defines a function of your second variable on all other variables. (a) What is the functional value of that function at 2? For example, my function would loe B(k, r). So the level curve would implicitly define r = r(k). This question is asking what is r(2). (b) Find the first-order partial derivative of that (second) variable with regard to the first variable at 2. With the notation of my example, the question is asking me to find r; at k = 2. (c) Find a linear approximation to the implicitly defined function in the proximity of the point 2. With the notation of my example, the question is asking me to find a linear approximation for r(k) for values clo to k = 2. (7) Test whether your function is homogeneous. If so of what degree? If not - how can you adjust your function to make it homogeneous? Make two different suggestions. (8) Test whether your function is homothetic. If it is make a formal argument. If it is not show a counterexample. Formal requirements: All submissions are individual submissions. Submissions must satisfy the following 10 formal requirements: You must properly credit all sources. Typed PDF format only. Text, doc, odt, or other formats are not accepted. Using a sansserif font (e.g. Calibri). 1 in margin, 11 pt setting, 1.15 spacing. Maximum length: 4 pages (incl. graphs). There is no minimum page requirement. Top right-hand corner of first page, include your first and last name, York ID, and email address. All formal expression must be properly formatted using the MS Word Equation editor, including those that are in line with the text. Consistent formatting throughout your document, e.g., using the same font. Satisfies minimal editing standards; Complete sentences, consistent tense, few if any passive sentences (10% of sentences or less), no obvious grammatical or spelling errors (that might be caught by MS Word), reasonable ease of readability (a score of 40 or higher)