18) The demand equation is x + 1/6p - 10+0.

Compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at p=50.

a) 5; elastic
b) 1/9; inelastic
c) 7/6; elastic
d) 6; elastic

I choose answer A. Is that correct?

To compute the elasticity of demand, we need to use the formula:

E = (dp/dx) * (x/p)

Here, x represents quantity demanded, p represents price, and dp/dx denotes the derivative of the demand equation with respect to x.

Given the demand equation: x + (1/6)p - 10 + 0

First, let's differentiate the demand equation with respect to x to find the derivative, dp/dx:

dp/dx = 1

Next, substitute the value of p = 50 into the demand equation and differentiate with respect to x:

x + (1/6)(50) - 10 + 0 = 0
x + 8.33 - 10 = 0
x - 1.67 = 0
x = 1.67

Now we can substitute the values of dp/dx and x/p into the elasticity of demand formula:

E = (dp/dx) * (x/p)
= 1 * (1.67/50)
= 1.67/50
≈ 0.0334

To determine whether the demand is elastic, unitary, or inelastic, we consider the magnitude of the elasticity value. If E < 1, the demand is inelastic; if E = 1, the demand is unitary; if E > 1, the demand is elastic.

In this case, E ≈ 0.0334, which is less than 1. Therefore, the demand is inelastic.

So, the correct answer is not A. The correct answer is b) 1/9; inelastic.

To determine the elasticity of demand, we can use the formula:

Elasticity of demand = (% change in quantity demanded) / (% change in price)

Given the demand equation: x + 1/6p - 10+0.

We can calculate the quantity demanded (x) at p = 50 as follows:

x + 1/6(50) - 10+0 = 0

x + 8.33 - 10 = 0

x = 1.67

Now, let's calculate the new quantity demanded when the price increases by 1 unit from 50 to 51:

x + 1/6(51) - 10+0 = 0

x + 8.5 - 10 = 0

x = 1.5

The % change in quantity demanded can be calculated as:

(% change in quantity demanded) = [(New quantity demanded - Original quantity demanded) / Original quantity demanded] * 100

(% change in quantity demanded) = [(1.5 - 1.67) / 1.67] * 100

(% change in quantity demanded) = (-0.17 / 1.67) * 100

(% change in quantity demanded) = -10.18%

Now, let's calculate the % change in price:

(% change in price) = [(New price - Original price) / Original price] * 100

(% change in price) = [(51 - 50) / 50] * 100

(% change in price) = (1 / 50) * 100

(% change in price) = 2%

Now, we can calculate the elasticity of demand:

Elasticity of demand = (% change in quantity demanded) / (% change in price)

Elasticity of demand = (-10.18% / 2%)

Elasticity of demand = -5.09

Since elasticity is a positive value, we can drop the negative sign, resulting in an elasticity of 5.09.

Since the elasticity of demand is greater than 1, the demand is elastic.

Therefore, the correct answer is not (a) 5; elastic.