Preview File Edit View Go Tools Window Help PS1.pdf (page 1 of 2) Q Search 2. De

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Preview File Edit View Go Tools Window Help PS1.pdf (page 1 of 2) Q Search 2. Definition: Let K be an integer. The function g : RK +2 R is homogeneous of degree m in r ER and y E R if and only if g(Az. xy, z) = 'ng(z, y, z) for all E R, and z E RK. Euler's Theorem: Suppose that g: RK+2 R is continuously differentiable in x E R and y R, with partial derivatives denoted by 9r and gy is homogeneous of degree m in r and y Then mg(x, y,2) -9r(r, y, z)r 9y(x, y, )y for all e R, y E R and zERK Moreover, 9x(x, y, z) and gyx, y, z are themselves homogeneous of degree m -1 in r and y (a) Prove Euler's Theorem. (b) Think about a production function F(K, XN) which is strictly increasing, strictly con cave, homogeneous of degree 1, and satisfies Inada conditions. Define k - and f(k) = F(KNN) Show that /0K = f,(k). Then solve for 0F/0 V, also express it by k and f(k) (c) Suppose F also satisfies F(0, XN) 0 and F(K, 0) 0 show that link-0 f(k)/k = oo and lim++ f(k)/k = 0 ngi ng ·13

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Marginal analysis involves a cost-versus-benefits comparison of various business activities. In marginal analysis, the cost of an activity is measured against incremental changes in volume to determine how the overall change in cost will affect the bottom line of a business. Marginal analysis can show the cost of additional production by a business all the way up to the break-even point. This is generally the maximum cost that a business can sustain without losing money.

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