Consider a duopoly in which both firms produce exactly the same product

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Consider a duopoly in which both firms produce exactly the same product. Suppose the firms' total cost functions are given as follows:

[Math Processing Error]TC1(Q1)=10Q1

[Math Processing Error]TC2(Q2)=10Q2

The market demand is given by [Math Processing Error]P=20−12Q.

A. In a price competition game, what price should be optimally set by each firm? How much will be sold by each firm?

B. In a quantity competition game, what quantity should be set by each firm? What will be the market price?

C. If both firms decide to collude, how much should each firm optimally produce? What will be the market price?

D. In which case do firms enjoy a larger profit margin? Explain.