Input: A new craft brewer has opened its doors in Newtown and is offering samples of its latest brew, The Hopolators Delight, at a price of$9.00 each. the market demand curve would be p = 3020 - 320q, what is the absolute value of own price elasticity of demand for the market at the equilibrium?

First, we need to find the equilibrium quantity (q) by setting the price (p) equal to $9 in the market demand equation:

9 = 3020 - 320q

Solving for q gives us:

q = (3020 - 9) / 320 = 9.41

The formula for the own price elasticity of demand is:

E = (dq/dp) * (p/q)

Where:

• dq/dp is the derivative of the demand function with respect to price, which in this case is -320 (from the demand equation p = 3020 - 320q)
• p is the price, which is $9
• q is the quantity, which is 9.41

Substituting these values into the formula gives us:

E = (-320) * (9/9.41) = -304.57

The absolute value of this is 304.57, so the own price elasticity of demand for the market at the equilibrium is 304.57. This means that a 1% increase in price would lead to a 304.57% decrease in quantity demanded, indicating that demand is highly elastic.