a) Find the first derivative. Based on your answer, discuss the function in terms of being...
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a) Find the first derivative. Based on your answer, discuss the function in terms of being increasing/decreasing, its convex or concave properties. b) Find the second derivative. Based on your answer, discuss if the function is convex or concave. c) (Bonus: 2 points) In applying mathematical methods to economics/business problems, we use a broad menu of functions to accurately specify the properties of the economic variables in question. Provide an example that demonstrates the use of the given function to describe a certain economic or business activity. 2. (20 points) Elon Musk asks you to invest $10M in his new cyber scooter product. He promises that he will return $15M to you at the end of the next 5 years. On the other hand, your good friend and hedge fund manager Jim Simons wants you to invest in his new fixed income fund. Jim promises that your money with $10M will be continuously compounded over the next 5 years. At what interest rate would Jim's offer be better than that of Elon's? 3. (20 points) The market for a particular good can be described by the equations: Qa = 20-4P Qs=2+P-w Qs = Qa = Q Where Q and P are respectively the equilibrium quantity and price, w is the current wage of labor used for production. a) Use repeated substitution to solve for the equilibrium Q and P as a function of w. b) Based on a), find the first derivative of function P(w). c) (Bonus: 3 points) Discuss the impact of a $1 increase in wage on price P. a) Find the first derivative. Based on your answer, discuss the function in terms of being increasing/decreasing, its convex or concave properties. b) Find the second derivative. Based on your answer, discuss if the function is convex or concave. c) (Bonus: 2 points) In applying mathematical methods to economics/business problems, we use a broad menu of functions to accurately specify the properties of the economic variables in question. Provide an example that demonstrates the use of the given function to describe a certain economic or business activity. 2. (20 points) Elon Musk asks you to invest $10M in his new cyber scooter product. He promises that he will return $15M to you at the end of the next 5 years. On the other hand, your good friend and hedge fund manager Jim Simons wants you to invest in his new fixed income fund. Jim promises that your money with $10M will be continuously compounded over the next 5 years. At what interest rate would Jim's offer be better than that of Elon's? 3. (20 points) The market for a particular good can be described by the equations: Qa = 20-4P Qs=2+P-w Qs = Qa = Q Where Q and P are respectively the equilibrium quantity and price, w is the current wage of labor used for production. a) Use repeated substitution to solve for the equilibrium Q and P as a function of w. b) Based on a), find the first derivative of function P(w). c) (Bonus: 3 points) Discuss the impact of a $1 increase in wage on price P.
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Managerial economics applications strategy and tactics
ISBN: 978-1439079232
12th Edition
Authors: James r. mcguigan, R. Charles Moyer, frederick h. deb harris
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