Question

Use the​ price-demand equation p plus 0.005 x equals 46​, 0 less than or equals p less than or equals 46. Find the elasticity of demand when pequals​$22. If the ​$22 price is decreased by 12​%, what is the approximate percentage change in​ demand?

Answer 1

To find the elasticity of demand, substitute the price value into the equation and solve for x. Then, use the formula for percentage change in demand to calculate the approximate percentage change in demand when the price decreases by 12%.

Step-by-step explanation:

To find the elasticity of demand, we need to use the price-demand equation p + 0.005x = 46. Given that p = $22, we can substitute this value into the equation:

$22 + 0.005x = 46

Subtracting $22 from both sides, we get:

0.005x = 24

Dividing both sides by 0.005, we find that x = 4800.

To find the approximate percentage change in demand when the price decreases by 12%, we can use the formula:

Percentage change in demand = (Change in demand / Original demand) × 100

Original demand is given by x = 4800. The change in demand can be calculated as:

(12/100) × 4800 = 576

Therefore, the approximate percentage change in demand is 576 / 4800 × 100 = 12%.

Answer 2

a. -0.92

b. 11% increase in demanded

Step-by-step explanation:

Given p + 0.005x = 46, 0 ≤ p ≤ 46

Rewriting the demand equation by solving for x as follow:

0.005x = 46 - p

x = (46 - p) / 0.005

x = (46 / 0.005) - (1/0.005)p

x = 9,200 - 200p .................................................................... (1)

Differentiating equation (1) with respect to p, we have:

dx/dp = -200

We can now answer the two questions as follows:

a. Find the elasticity of demand when pequals$22.

To calculate elasticity of demand, the formula for calculating the elasticity of demand is used as follows:

E = Elasticity of demand = (p / x) * (dx / dp) ................... (2)

Since p = $22, we find x in equation (1) by substituting for p as follows:

x = 9,200 - 200 (22) = 4,800

Note that dx/dp = -200

Substituting the values into equation (2), we have:

E = (22 / 4,800) * (-200) = -0.92

Note: Since the absolute value of E i.e. |-0.92| is less than one, the demand is inelastic.

If the ​$22 price is decreased by 12​%, what is the approximate percentage change in​ demand?

To do calculate this, we use the following formula for calculating the elasticity of demand:

E = % change in demand / % change in price ............. (3)

Since,

E = - 0.92

% change in price = -12%, or -0.12

Substituting the values into equation (3) and solve for % change in demand, we have:

-0.92 = % change in demand / -0.12

% change in demand = [-0.12] * [-0.92] = 0.11, or 11%

Therefore, the approximate percentage change in​ demand if the ​$22 price is decreased by 12​% is 11% increase in demand.