Final answer:
To calculate the elasticity of demand at a price of $31, substitute the price into the demand equation to find the quantity. Then, calculate the percentage change in quantity. Finally, substitute the values into the elasticity formula to find the elasticity.
Step-by-step explanation:
To calculate the elasticity of demand, you need to use the formula:
E = (% change in quantity) / (% change in price)
For this question, the price is $31 and the demand equation is D(p) = -3p + 210. So, we need to find the quantity when the price is $31 and then calculate the elasticity.
First, substitute p = 31 into the demand equation to find the quantity:
D(31) = -3(31) + 210 = 147
Next, calculate the percentage change in quantity:
% change in quantity = (147 - 210) / ((147 + 210) / 2) * 100
Finally, substitute the values into the elasticity formula:
E = (% change in quantity) / (% change in price)
E = ((147 - 210) / ((147 + 210) / 2)) / ((31 - 210) / ((31 + 210) / 2))
E = -0.56