L16_derivatives_6_gaps

L16_derivatives_6_gaps - 1 1 Lecture 16: Topic:...

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Unformatted text preview: 1 1 Lecture 16: Topic: Differentiation Reading for this lecture H&P, Ch 11, Sect 11.5. Homework for Tutorial in Week 7 Ex 11.5, pp. 521-523, problems 5, 21, 29, 55, 65, 71. 2 Chain Rule Given y = f(u) and u = g(x). dy = dy du dx du dx Example If y = (4x +2 ) 3 Then let u = 4x + 2 so that y = u 3 dy = 3u 2 and du = 4 du dx dy = 3u 2 (4) = 3(4x + 2) 2 (4) = 12(4x + 2) 2 dx 3 Example y = (2x 2 + 3) 4 4 is the additional revenue obtained from the sale of the output resulting from hiring one more unit of an input. Suppose m units of labour produce q units of output according to the production function: q = g(m) A perfectly competitive firm sells each unit of output at a price, p ( p is constant ). The total revenue function is R = pq Marginal-revenue product, MRP = Marginal-Revenue Product 5 Suppose a perfectly competitive firm can produce q units of output m with units of labour according to the production function: q = 100m ½ The firm sells each unit of output for $5....
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L16_derivatives_6_gaps - 1 1 Lecture 16: Topic:...

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