HSC Commerce Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

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?

The supply function of certain goods is given by x = a`sqrt("p" - "b")` where p is unit price, a and b are constants with p > b. Find elasticity of supply at p = 2b.

Show that MR = p`[1 - 1/eta_"d"]` for the demand function p = 400 – 2x – 3x² where p is unit price and x is quantity demand.

For the demand function p = 550 – 3x – 6x² where x is quantity demand and p is unit price. Show that MR = 

Find the values of x, when the marginal function of y = x³ + 10x² – 48x + 8 is twice the x.

For the demand function x = `25/"p"^4`, 1 ≤ p ≤ 5, determine the elasticity of demand.

The demand function of a commodity is p = `200 - x/100` and its cost is C = 40x + 120 where p is a unit price in rupees and x is the number of units produced and sold. Determine

1. profit function
2. average profit at an output of 10 units
3. marginal profit at an output of 10 units and
4. marginal average profit at an output of 10 units.

The total cost function y for x units is given by y = 3x`((x+7)/(x+5)) + 5`. Show that the marginal cost decreases continuously as the output increases.

Find the price elasticity of demand for the demand function x = 10 – p where x is the demand p is the price. Examine whether the demand is elastic, inelastic, or unit elastic at p = 6.

Find the equilibrium price and equilibrium quantity for the following functions.
Demand: x = 100 – 2p and supply: x = 3p – 50.

The demand and cost functions of a firm are x = 6000 – 30p and C = 72000 + 60x respectively. Find the level of output and price at which the profit is maximum.

The cost function of a firm is C = x³ – 12x² + 48x. Find the level of output (x > 0) at which average cost is minimum.

The total cost function for the production of x units of an item is given by C = 10 - 4x³ + 3x⁴ find the

1. average cost function
2. marginal cost function
3. marginal average cost function.

Find out the indicated elasticity for the following function:

p = xe^x, x > 0; η_s

Find out the indicated elasticity for the following function:

p = `10 e^(- x/3)`, x > 0; η_s

Find the elasticity of supply when the supply function is given by x = 2p² + 5 at p = 1.