Assume that the market for electricity in the UK is duopolistic and the demand is given by: P=200-20Q, where: Q=q1+q2 (i

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Assume that the market for electricity in the UK is duopolistic
and the demand is given by: P=200-20Q, where: Q=q1+q2 (inverse
demand function). The total cost function for each
is .
The total cost function for each firm has the production capacity
to cover all demand. Output choices are made sequentially. First,
firm1 decides irreversibly over output, and then observing firm 1's
output, firm 2 chooses its output.
1) Calculate the Stackelberg equilibrium output, price and
profits for each firm.
2) Compare both firms' profits and discuss your result. Present
the Stackelberg equilibrium output in a diagram.
3) Assuming that inverse demand is now given by:
while all other assumptions and functions remain the same as
before, calculate the equilibrium price when firm 1 decides
irreversibly over price, and then after observing 1's price, firm 2
chooses it price.