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:
P=A- Kq1k-Rq2r 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.