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Basic Mathematics for Economists phần 3

nơi mà tất cả các công ty phải đối mặt với các chức năng chi phí trung bình trong đó q là sản lượng mỗi tuần. Chức năng này chỉ đề cập đến chi phí sản xuất. Sau đó, họ quyết định để khởi động một chiến dịch quảng cáo, chứ không phải chỉ để cố gắng tăng doanh số bán hàng nhưng cũng cố gắng để nâng cao tổng chi phí trung bình của mức sản lượng thấp | Test Yourself Exercise 4.8 1. Sketch the approximate shape of the following composite functions for positive values of all independent variables. a TR 40q - 4q2 b TC 12 4q 0.2q2 c n -12 36q - 3.8q2 d y 15 - 2x-1 e AVC 8 - 3q 0.5q2 2. Make up your own example of a composite function and sketch its approximate shape. 3. A firm is able to sell all its output at a fixed price of 50 per unit. If its average cost of production is given by the function AC 100x-1 0.4x2 where x is output derive a function for profit n in terms of x. What approximate shape will this profit function take 4. A small group of companies operate in an industry where all firms face the average cost function AC 40 1 250q-1 where q is output per week. This function refers only to production costs. They then decide to launch an advertising campaign not just to try to increase sales but also to try to raise the total average cost of low output levels and deter potential smaller-scale rival firms from competing in the same market. The cost of the advertising campaign is 2 000 per week per firm and any competitor would have to spend the same sum on advertising if it wished to compete in this market. a Derive a function for the new total average cost function including advertising and sketch its approximate shape. b Explain why this advertising campaign will deter competition if the original companies sell a 100 units a week at a price of 100 each and new competitors cannot produce more than 25 units a week. 4.9 Using Excel to plot functions It may not immediately be obvious what shape some composite functions take. If this is the case then it may help to set up the function as a formula on a spreadsheet and then see how the value of function changes over a range of values for the independent variable. Learning how to set up your own formulae on a spreadsheet can help you to in a number of ways. In particular spreadsheets can be very useful and save you a lot of time and effort when tackling problems .