EC4004 Economics Quantitatively Treated Assessment

Find the values of x at which the following functions take a local maximum or minimum value (if any):

1. y = -2x^2 + 20x
2. y= x^2 - 14x + 3
3. y = x^ 3 - 12x + 15
4. y = x^ 3 - 9x^2 + 27x - 27
5. A firm has a total revenue function : TR(Q) =-20Q -Q^2 and a total cost function: TC(Q) = 1/3Q^3 - 6Q^2 +29 Q +15 .
   • The firm’s profit maximizing level of output and the values of profit, price and revenue at this output level.
   • The revenue maximizing output level and the values of profit, price and revenue at this output level.
6. The output for a firm over time is given by the function: Q=T^3/30-T^2/5+3T/10+120

Find the years (t) in which the output is at a maximum and a minimum