Question

1. Calculus Practice
What are the derivatives of the following?
a. y = 2X2                                dy/dx = ______________
b. y = abXc                                dy/dx = ______________
c. U = XaYb                               du/dx = ______________;
                                   du/dy = ______________

d. Total Benefit = 100X - 2X2               Marginal Benefit =    ______________
e. Total Cost = -100X +   2X2               Marginal Cost =    ______________
What are the maxima/minima of the following?
f. Total Benefit = 100X - 2X2                   Maximum =    ______________
g. Total Cost = -100X +   2X2                   Minimum =    ______________

h. Suppose a firm had the total benefit and total cost curves as in d and e. What quantity level would maximize profits (where profits are total benefits - total costs)? __________________________
   You may solve this either by taking the derivative of the profit function, or by setting the marginal benefits=marginal costs, but I recommend your getting practice with both.

Answer 1