Applications of Differentiation in Business and Economics

A firm produces x tonnes of output at a total cost of C(x) = `1/10x^3 - 4x^2 - 20x + 7` find the

1. average cost
2. average variable cost
3. average fixed cost
4. marginal cost and
5. marginal average cost.

The total cost of x units of output of a firm is given by C = `2/3x + 35/2`. Find the

1. cost when output is 4 units
2. average cost when output is 10 units
3. marginal cost when output is 3 units

Revenue function ‘R’ and cost function ‘C’ are R = 14x – x² and C = x(x² – 2). Find the

1. average cost
2. marginal cost
3. average revenue and
4. marginal revenue.

If the demand law is given by p = `10e^(- x/2)` then find the elasticity of demand.

Find the elasticity of demand in terms of x for the following demand laws and also find the value of x where elasticity is equal to unity.

p = (a – bx)²

Find the elasticity of demand in terms of x for the following demand laws and also find the value of x where elasticity is equal to unity.

p = a – bx²

Find the elasticity of supply for the supply function x = 2p² + 5 when p = 3.

The demand curve of a commodity is given by p = `(50 - x)/5`, find the marginal revenue for any output x and also find marginal revenue at x = 0 and x = 25?