5. (Car Demand) We want to estimate the price clasticity in the automobile market. We collect data on 40 different cars' sales and price information in Beijing in May 2022, and want to estimate the following model: Si = Bo + Bipi + B2HP; + ui, where s, is the market share, p; is the retail price, and HP, is the horse power. Our interest is to get a consistent estimator for 81. (a) We are worried that a may contain unobserved quality, which might be correlated with p; because higher quality cars are more expensive. To address the issue, we plan to use the national steel price in May 2022 as an IV. The argument is that the steel price will affect the production costs of the car, thus will affect the car's retail price. Besides, car producers are price takers in the steel market, so the steel price is exogenous. Is this a valid IV? Explain. (5 points) (b) Suppose we find two instruments, , and 2, for price. Explain how you would test whether there exists weak instrument problem. (5 points) (c) Suggest a different IV than in (a) for this case and briefly explain why you think it is valid. (5 points)