Supply Function and Elasticity

The supply function of a commodity is given by: p = (x 40) /6, where p represents the price of the commodity and x represents the quantity supplied.

Elasticity of supply measures the responsiveness of quantity supplied to changes in price. It is calculated as the percentage change in quantity supplied divided by the percentage change in price.

Calculating Elasticity of Supply

To calculate elasticity of supply when x = 32, we need to find the derivative of the supply function with respect to price. This gives us the slope of the supply curve at x = 32, which is the marginal cost of producing an additional unit of the commodity.

The derivative of the supply function is: dp/dx = 1/6

Using the formula for elasticity of supply, we get:

Elasticity of supply = (dp/dx) * (p/x) = (1/6) * [(32-40)/32] = -1/3

Interpreting Elasticity of Supply

The elasticity of supply is negative because the supply function is downward sloping. However, we usually report the absolute value of elasticity, which is always positive.

The magnitude of elasticity tells us the extent to which quantity supplied changes in response to a change in price. An elasticity greater than 1 means that quantity supplied is highly responsive to price changes, while an elasticity less than 1 means that quantity supplied is not very responsive to price changes.

In this case, the elasticity of supply when x = 32 is:

|Elasticity of supply| = |-1/3| = 1/3

This means that quantity supplied is not very responsive to price changes, since the elasticity is less than 1.

Answer: C) 6.75