the demand for ground chuck(hamburger) in a certain region of the US is given by q= 3.41p^-0.22. is the demand for ground chuck elastic or inelastic
inelastic
To determine whether the demand for ground chuck in a certain region is elastic or inelastic, we need to examine the price elasticity of demand (PED).
The formula to calculate PED is:
PED = (% change in quantity demanded) / (% change in price)
To classify demand as elastic, inelastic, or unitary elastic, we compare the absolute value of the PED to 1:
- If PED > 1, the demand is considered elastic.
- If PED < 1, the demand is considered inelastic.
- If PED = 1, the demand is considered unitary elastic.
Let's calculate PED using the given demand function, q = 3.41p^(-0.22):
Let's assume the price of ground chuck increases by x%, and as a result, the quantity demanded decreases by y%. Using this information, we can plug in the values into the PED formula.
PED = (y / x) * (1 / (q/p))
As the equation becomes complex, let's simplify it before calculating. Using the properties of exponents, we can rewrite the demand function as follows:
q = 3.41 * p^(-0.22) = 3.41 / p^(0.22)
Now, let's differentiate both sides of the equation with respect to p to find dq/dp:
dq/dp = -3.41 * 0.22 * p^(-1 - 0.22) = -0.75p^(-1.22)
Next, let's substitute dq/dp and the given values into the PED formula:
PED = (y / x) * (1 / (q/p)) = (y / x) * (p / dq/dp)
PED = (y / x) * (p / (-0.75p^(-1.22))) = (-y / x) * (4 / 3p^(0.22))
Since we are only interested in identifying whether the demand is elastic or inelastic, we don't need to calculate a specific value for PED. We can analyze its behavior based on the expression derived.
From the expression, we observe that PED contains the factor (-y / x). The negative sign doesn't affect the elasticity classification. Instead, we analyze the absolute value of PED.
If |PED| < 1, the demand is inelastic. (Since (-y / x) is a positive value)
If |PED| > 1, the demand is elastic. (Since (-y / x) is a positive value)
Based on the given demand function q = 3.41p^(-0.22), we can conclude that the demand for ground chuck in this certain region is elastic since the PED is greater than 1.