QUESTION 3: JUICY OPPORTUNITIES (40 POINTS) In 2022, the total demand for batteries by electric vehicle manufacturers is given by QB = 500 5UP, where Q is measured in hundreds of thousands of batteries and P 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 0(6)) = 40 + 0.1 x if)". Moreover, competition among these manufacturers is such that they are all price takers. (a) [8 points] Based on the cost function above, identify the xed, variable, average, and marginal costs of a typical EV battery manufacturer. (b) [8 points] Compute the supply curve for each manufacturer; that is, for any price P, what is the quantity Q1 that an individual manufacturer will optimally produce to maximize prots? (c) [5 points} Suppose that there are 10 active EV battery manufacturers. Compute the aggregate supply curve for EV batteries; that is, for any price P, what is the total quantity Q3 that is collectively produced by all ten manufacturers? (d) [7 points] Assuming perfect competition among the 10 active manufacturers, what is the short run equilibrium price and quantity of EV batteries? (e) [4 points] Given these market conditions, would you expect entry or exit to occur? Explain. (f) [8 points] Assuming that demand remains stable going forward, how many manufacturers do you expect to see in this market in the long run