Math for Econ I, Homework Assignment 2 Instructor: Antonio De Rosa Due: Thursday, September 21st, during Lecture New York University Instructions: IMPORTANT: PLEASE WRITE THE NUMBER OF YOUR RECITATION SECTION (NOT ONLY THE CLASS SECTION NUMBER 006)! IT WILL BE IMPORTANT TO GIVE YOU BACK THE HOMEWORKS DURING THE RECITATION YOU ATTEND! If you have the textbook, please read chapter 4, especially sections 4.5 through 4.9 and compare with the slides of Lecture 4. Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work you will not be given any credit. Write your name and recitation section number. Staple your homework if you have multiple pages! 1. (7 pts) A firm produces mobile phones and receives $200 for each unit sold. The cost of producing and selling x units is 10x + x2 dollars. (a) (2 pts) Write the profit as a function of the number of units sold. (b) (2 pts) Find the production level which maximizes the profit (in other words, find the x that maximizes the profit function). (c) (3 pts) A tax of $10 per unit is imposed on the firm. What is the new cost function? What is the new optimum production level? 2. (9 pts) A person is to be paid for a work. Three payment options are being considered. Option 1 is to pay him $1600 now. Option 2 is to pay $900 now and $900 in a year. Option 3 is to pay $2000 in a year. Assume an annual interest rate of 5% a year, compounded continuously. (a) (3 pts) Compute how much money the person will have, in one year's time, for all three options. (b) (3 pts) Which option is the best option financially for the worker? Explain. (c) (3 pts) Compute how much money the person will have, in one year's time, for all three options in case the interest rate was compounded annually (once a year). 3. (4 pts) Consider the function y(x) = 10x . 105 x (a) (2 pts) Roughly sketch its graph. (b) (2 pts) Label all intercepts and all horizontal or vertical asymptotes that exist