ECON 2P91 Lecture : Lecture 3

Robinson has a production function of 2C+F=8 and Friday has a production function of C+F=4. The opportunity cost for Robinson is 1F=.5C and 1C=2F. Friday has an opportunity cost of 1F=1C. If each specialize Robinson will produce C and Friday will produce F. How do you determine how much each will produce after they specialize? How do you determine how much each will trade and what happens after trade?

Question 3. (20 marks) Let y = f(2) be defined by f(1) = ln(2 + 1-3). (a) For what values of is f(1) defined? (b) Show that f(r) is strictly increasing. Hint: find f'(2). (c) What is the range of f(x)? (d) Find the inverse function, g(y). (e) For what values of y is g(y) defined? (f) Find t'y). (g) Verify that f(3) = 1/!'((3)).

Question 3. (25 marks) Let y = f(1) be defined by f(x) = ln(22 – 4). (a) Solve for r when f(0) = 0. (b) Use a sign diagram to determine the values of r for which fr) is defined. (c) Derive f'(.). (d) Use f'(x) to determine when f(x) is increasing and/or decreasing. (e) Derive and use f" () to show if f(x) convex or concave.