Suppose the total cost function of a firm is given by C=3q1³+7q1+1..5q1q2+6q2+2q2²
The total cost function of the firm can be expressed as:
C = 3q1³ + 7q1 + 1.5q1q2 + 6q2 + 2q2²
In this function, q1 represents the quantity of input 1 used by the firm and q2 represents the quantity of input 2 used by the firm.
The first term, 3q1³, represents the cost associated with input 1. This term indicates that as the quantity of input 1 increases, the cost associated with it increases exponentially. The coefficient 3 signifies the rate of increase.
The second term, 7q1, represents the linear cost associated with input 1. This term indicates that as the quantity of input 1 increases, the cost associated with it also increases linearly. The coefficient 7 signifies the rate of increase.
The third term, 1.5q1q2, represents the cost associated with the interaction between input 1 and input 2. This term indicates that the cost depends on the joint usage of both inputs. The coefficient 1.5 signifies the rate of increase.
The fourth term, 6q2, represents the linear cost associated with input 2. This term indicates that as the quantity of input 2 increases, the cost associated with it increases linearly. The coefficient 6 signifies the rate of increase.
The fifth term, 2q2², represents the cost associated with input 2 squared. This term indicates that the cost of input 2 increases at an accelerating rate as its quantity increases. The coefficient 2 signifies the rate of increase.
Overall, this total cost function captures the cost structure of the firm in terms of the quantities of both input 1 and input 2 used.