The demand function for price increases and for price cuts for an oligopolist are, respectively,

Q₁= 210 - 30P₁or P₁= 7 - Q₁/30

Q₂= 90 - 10P₂or P₂= 9 - Q2/10

The oligopolist's total cost function is: TC = 3.5Q + Q²/60

(a) Derive the MR₁, MR₂, and MC functions facing the oligopolist.

(b) Determine the price and output at the kink on the demand curve.

(c) Determine the upper and lower limit of the MR gap and prove that MC falls in the MR gap.

(d) Find the value of the total profits of the oligopolist.