Suppose there are n hunters trying to hunt mammoths. The total number of mammoths hunted by hunters depends on how much effort the hunters give. Suppose the effort of a hunter is called 'qi' and is equal to or greater than zero (qi 0). The sum of all hunters' efforts is said to be Q=q1+q2+...+qn. The total number of mammoths hunted is defined as Q* (1000-Q). The above expression contains two factors. Given the size of a given mammoth, the number of mammoths hunted increases as hunter efforts increase. However, as the population decreases and the number of mammoths that can be reproduced decreases, the number of mammoths that can be hunted decreases as hunter efforts increase. Also, the amount of mammoth meat received by hunter 'i' is equal to the percentage of effort made by hunter 'i' in the entire hunter's effort. Suppose the hunter 'i' spends on hunting mammoths.

(a) Find the complement function V(q1,q2,...qn) of the hunter'i'.

(b) Find the best response function of hunter'i'.

(c) Find the Nash Equilibrium.

(d) Suppose you are hunting too many mammoths. In other words, hunters are hunting mammoths beyond the amount of mammoth meat that maximizes utility. Assume that meat production maximizes utility when the total hunter's effort is 500. Find the number of hunters who can optimize meat production.