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# Partial elasticity of demand

Let q = f( p1, p2) be the demand for commodity A, which depends upon the prices

Partial elasticity of demand

Let q = f( p1, p2) be the demand for commodity A, which depends upon the prices

p1 and p2 of commodities A and B respectively.

The partial elasticity of demand q with respect to p1 is defined to be The partial elasticity of demand q with respect to p2 is defined to be Example 6.40

Find the marginal productivities of capital (K) and labour (L) if

=10L + 0.1L2 + 5K - 0.3K2 + 4KL when K=L=10.

Solution:

We have P = 10L + 0.1L2 + 5K - 0.3K2 + 4KL Example 6.41

The production function for a commodity is P=10L + 0.1L2 + 15K - 0.2K2 + 2KL where L is labour and K is Capital.

(i) Calculate the marginal products of two inputs when 10 units of each of labour and Capital are used

(ii) If 10 units of capital are used, what is the upper limit for use of labour which a rational producer will never exceed?

Solution:

(i) Given the production is P = 10L ŌłÆ 0 . 1L2 +15K ŌłÆ 0 .2K2 + 2KL (ii)  Upper limit for use of labour when K=10 is given by a 22PL k Ōēź0

10 ŌłÆ 0.2L+20 Ōēź0

30 Ōēź 0.2L

i.e.,L Ōēż 150

Hence the upper limit for the use of labour will be 150 units

Example 6.42 Exercise 6.5  Tags : Applications of partial derivatives , 11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation
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11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation : Partial elasticity of demand | Applications of partial derivatives