Raymond B. answered • 03/29/21
Math, microeconomics or criminal justice
P+7q = 280 is the demand curve. It's downward sloping, linear, with x or q intercept of 40 and y or P intercept of 280. At P=280, nothing is sold. at P=0, they can't give away more than 40.
At P=140, they sell 20.
elasticity of demand = %change in q divided by %change in P = (P/Q)(dQ/dP)
solve for q,
7q = 280-P
q = 40-P/7
dq/dP = -1/7
P/Q)(dq/dP) = (140/20)((-1/7) = -1 or unit elasticity
convention is to ignore the negative sign and just say elasticity of demand = 1
also the terminology is "price elasticity of demand" to distinguish it from income elasticity or cross price elasticity of demand. This problem also involves point elasticity, as opposed to calculating the elasticity over an interval.
since the demand curve is almost always considered downward sloping the price elasticity of demand is always negative, so convention is to just ignore the sign as it's understood to be negative (except for a Giffen good, a strange exception)
