Answer to Question 1
It is difficult to set a fair price in a monopolized market. Antitrust authorities can either set a price in the market that is equal to marginal cost or can require firms to set a price that is equal to average cost. The price set at marginal cost is called the efficient price or the socially-optimal price. While this is the price at which social surplus is maximized, in a natural monopoly, marginal cost is lower than average total cost at every quantity. So, at this price, the firm will experience an economic loss and will eventually exit the industry. Alternatively, the government could require firms to set the price at average total cost. This would allow the monopolist to stay in business as the firm would not incur losses. However, both these forms of price regulation would mean that the firm has no incentive to minimize costs or to innovate and produce new goods and services.
Answer to Question 2
Utility is the satisfaction (or reward) a product yields relative to its alternatives. It is the basis of choice.
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Finding the derivative using the power rule - Solutions
Differentiate each function with respect to x. (Power rule)
Power Grip and Precision Grip