PracticeQuestion4 econ 326.pdf

# PracticeQuestion4 econ 326.pdf - Econ 326 Practice Question...

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Econ 326 Practice Question 4 (Chapter 9) Heejeong Kim 1. Which of the following quadratic functions are strictly convex? (a) y ( x ) = 9 x 2 - 4 x + 8 (b) u ( x ) = 9 - 2 x 2 (c) y ( x ) = - 3 x 2 + 39 (d) v ( x ) = 8 - 5 x + x 2 2. Consider f ( x ) = 3 x 2 3 - 5 x for x > 0. Find the first-order condition and solve. Show that your solution is a global maximizer. Is the function globally increasing or decreasing? 3. Consider f ( x ) = x 3 3 - 2 x 2 + 3 x + 7 for x 0. Find the solution to the first-order condition and determine if the solution is a local maximizer or minimizer. Where is the global maximum or global minimum? 4. Consider the function f ( x ) = x a - x b for x > 0 where 0 < a < 1 and b > 1. Solve the first-order condition and show that this is a global maximizer. 5. A firm has the following total-cost and demand functions C = 1 3 Q 3 - 7 Q 2 + 111 Q + 50 Q = 100 - P (a) Write out the total-revenue function R in terms of Q .

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(b) Formulate the total-profit function π in terms of Q . (c) Find the profit-maximizing level of output Q * .
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