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Applications of partial derivatives - Partial elasticity of demand | 11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation

Chapter: 11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation

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 0 . 1L2 +15K 0 .2K2 + 2KL


(ii)  Upper limit for use of labour when K=10 is given by a 22PL k ≥0

10 0.2L+20 ≥0

30 ≥ 0.2L

i.e.,L ≤ 150

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

 

Example 6.42


 

Exercise 6.5





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11th Business Mathematics and Statistics(EMS) : Chapter 6 : Applications of Differentiation


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