3. Microprocessors are a ubiquitous component of modern automobiles; an average modern automobile contains over 1400 small semiconductors ('chips'), controlling everything in the vehicle from ignition timing and transmission shifting to power door locks. These chips are produced mainly in East Asia by many firms, none of which have more than 10% market share; thus, we can consider this industry approximately perfectly competitive. Moreover, chips do vary in complexity, cost and ease of manufacture, but we shall simplify away from this and consider chips a standard, commoditized product. Suppose the demand for chips for use in automobiles is given by Q = 1,100,000,000 - 40,000,000 x P, where P is the price of a chip in US dollars and Q is the quantity of chips demanded per year. Chips are produced in 50 factories worldwide, each factory with a production capacity of 20 million chips per year. Each factory has overhead and assorted nonrecoverable fixed costs of $8 million per year. Factories do vary somewhat in their variable cost of production per chip; for simplicity, we shall suppose that there are 25 "low cost' factories with variable costs of $1.20 per chip and 25 'higher cost' factories with variable costs of $1.50 per chip. These data are summarized below. Supplier type Low cost Higher cost Variable costs Fixed costs Capacity $1.20 $1.50 $8,000,000 20,000,000 $8,000,000 20,000,000 Number of firms 25 25 a. What is the equilibrium price of a chip? How many chips are produced per year? b. In the spring of 2020, the start of the COVID-19 pandemic was predicted to disrupt global economies on an unprecedented scale. The demand for automobiles, and thus for automotive chips, was forecast to decrease by 25%. Thus, we can suppose a new demand function of Q = 825,000,000 30,000,000 x P. Given this consensus forecast of demand, several chip manufacturers chose to shut down. With this demand curve, what will be the equilibrium price of a chip? How many low-cost chip manufacturers will continue operating? How many higher cost manufacturers will continue operating? c. There was a brief drop in demand for automobiles and automotive chips, but demand recovered much more rapidly than analysts had anticipated. However, by the time this occurred, several firms had already shut down operations and could not restart production rapidly. Suppose the number of firms operating in the chip industry is as you calculated in part b above, but the demand function has returned to the original demand function of part a above. In this scenario, what price do you predict for automotive chips? d. Supply in the industry was further disrupted by a fire at a chip factory in Taiwan that destroyed the factory and prevented production there. Starting from the situation you analyzed in part c above, suppose one low-cost factory is destroyed. What do you anticipate will be the new equilibrium price of a chip?