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?
What you have written in not an equation.
Is one of your + or - signs supposed to be an = ?
in = is
To compute the elasticity of demand, you need to differentiate the demand equation with respect to the price (p) and then multiply it by the ratio of the price and quantity demanded.
First, let's differentiate the demand equation with respect to price (p):
d/dp(x + (1/6)p - 10) = 1/6
Next, we need to calculate the ratio of price (p) and quantity demanded (x). At p = 50, the demand equation becomes:
x + (1/6)(50) - 10 = x + 8.33 - 10 = x - 1.67
Now, we can calculate the elasticity of demand:
Elasticity of demand = (d/dp(x + (1/6)p - 10)) * ((p/x) = (1/6) * (50 / (x - 1.67))
Since the question asks for the elasticity at p = 50, we can substitute p = 50 into the equation:
Elasticity of demand = (1/6) * (50 / (x - 1.67))
Given the options, we can check which one matches this expression.
a) 5; elastic: (1/6) * (50 / (x - 1.67)) = 1/6 * (50 / (x - 1.67)) = 5 * (1/(x - 1.67)) != 5
b) 1/9; inelastic: (1/6) * (50 / (x - 1.67)) = 1/6 * (50 / (x - 1.67)) = 1/9 * (3/(x - 1.67)) != 1/9
c) 7/6; elastic: (1/6) * (50 / (x - 1.67)) = 1/6 * (50 / (x - 1.67)) = 7/6 * (1/(x - 1.67)) != 7/6
d) 6; elastic: (1/6) * (50 / (x - 1.67)) = 1/6 * (50 / (x - 1.67)) = 6 * (1/(x - 1.67)) != 6
Therefore, none of the given options match the calculated expression. The correct answer is not provided in the options provided.