If consumption c depends upon income y and liquid

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! If consumption, C , depends upon income, Y , and liquid assets, M : C = f (Y, M) = " + \$ Y + ( M where ( is the Greek letter gamma (i.e. not Y ), the marginal propensity to consume is the partial derivative of C with respect to Y keeping M fixed: ! Similarly, partially differentiating Y with respect to M gives: ( which measures the liquid assets sensitivity of consumption , ie. how consumption reacts to a change in liquid assets, M , keeping total income, Y , fixed. (ii) If output Y is given by the Cobb-Douglas production function where K represents capital, L represents labour, and A , " and \$ are “parameters”: Y = f ( K, L ) = A K L " \$ then the marginal products for capital and labour are:

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69 (iii) To partially differentiate y with respect to x , we treat the term in z as fixed, i.e. as a constant: To partially differentiate y with respect to z , we treat the term in x as fixed, i.e. as a constant: (iv) Using the alternative function notation: Treating the term inside brackets as constant: Similarly, to partially differentiate with respect to z:
70 (v) (vi) TUTORIAL EXERCISES 33. Partially differentiate the following functions using appropriate notation. (i) (iii) (ii) (iv) (v) 34. The elasticities of production for capital and labour are defined as: and Show that they are both constant for the Cobb-Douglas production function given by, Y = f ( K, L ) = A K L " \$
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