Consider a market characterized by the following inverse demand function: P=150-Q, where Q is the total amount produced in the market and P is the market price measured in dollars. For full credit, you must show all the steps of your calculations and explain what you are doing in each question to find the market equilibrium in each situation. Make sure you indicate the units of your variables when appropriate.

a) Suppose that the market is perfect competitive. What is the optimal market price and optimal market amount if the marginal cost is $30?

b) Now consider the case when the market has just one firm. The marginal cost is $30. What is the optimal market quantity and optimal market price?

c) Suppose the market has two firms - firm 1 and firm 2 - with symmetric cost functions and a homogeneous product. Each cost function equals TC=30q, where q is the quantity produced by a firm. What is the optimal market quantity and optimal market price if both firms compete simultaneously in quantities?

d) Suppose the market has two firms - firm 1 and firm 2 - with symmetric cost functions and a homogeneous product. Each cost function equals TC=30q, where q is the quantity produced by a firm. What is the optimal market quantity and optimal market price if both firms compete simultaneously in prices?

e) Suppose the market has two firms - firm 1 and firm 2 - with symmetric cost functions and a homogeneous product. Each cost function equals TC=30q, where q is the quantity produced by the firm. What is the optimal market quantity and optimal market price if these firms compete sequentially in quantities and firm 1 moves first?

f) Represent in just one graph the MARKET equilibrium for a) to e). Calculate the consumer surplus for each case. Comment on your results.