In 2023, the total demand for batteries by electric vehicle manufacturers is given by = 600 75, where is measured in hundreds of thousands of batteries and is the price (in thousands of dollars) per EV battery. Assume that all EV battery manufacturers produce identical batteries using the same technology. Each manufacturer has the same cost function of () = 20 + 0.2 2. Moreover, competition among these manufacturers is such that they are all price takers.

(a)Based on the cost function above, identify the fixed, variable, average, and marginal costs of a typical EV battery manufacturer. (b) Assume that each manufacturer is (at least in the short term) active in the market. Given any fixed market price , what is the optimal quantity that an individual price-taking manufacturer will produce to maximize profits? (c)Suppose that there are 10 active EV battery manufacturers. Compute the aggregate supply curve for EV batteries; that is, given any fixed market price , what is the total quantity that is collectively supplied by all ten manufacturers? (d) Assuming perfect competition among these 10 active manufacturers, what is the short run equilibrium price and quantity of EV batteries? (e) Given these market conditions, would you expect firms to enter or exit the market in the long run? Explain. (f) Assuming that demand remains stable going forward, how many manufacturers do you expect to see in this market in the long run?