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The sales of Laptops increased exponentially during the Covid Crisis

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The sales of Laptops increased exponentially during the Covid Crisis. It was observed that membership to internet services, Zoom also increased as well. Lenovo Laptops are widely considered to be the one of the top industry leaders in sales of Laptops. It's sleek design and light-weight makes it popular among students and professional alike. Lenovo competes with other similar brands and can be classified operating under the conditions of monopolistic competition. 

An economist estimates the demand function as P = 1250 - 7.5 Q, where P is in dollars and Q is in number of Lenovo Laptops sold per week. She also estimates the weekly expenses vary with output according to the following cost equation: 

TC = 10,000 + 25Q - 7.5Q² + 1/3 Q³.

1. Determine the firm's short-run profit-maximizing price and output rate.
2. What are the firm's fixed and variable cost? What are the firm's total revenues and total costs?  Is this firm making an economic profit, economic loss or a normal profit?
3. Suppose intense competition brings down prices and revenues. Calculate at what prices will the firm for each of the following cases: 3a) Make a normal profit?  3b) Incurs a loss but should continue to produce in the short run? 3c) Incurs a loss but should shut down?