Inelasticity question question, quantity, supplied, elastic, change

redskins44

When the price changes from $1.99 per gallon of milk to $3.25 per gallon, the quantity supplied did not change. the supply of milk in the United States is closest to being:
A. perfectly elastic, elasticity of supply=0
B. perfectly elastic, elasticity of supply=infinity
C. perfectly inelastic, elasticity of supply=0
D. perfectly inelastic, elasticity of supply=infinity
The book says answer C, but why is the slope equal to 0? I would think (looking at the graph and remembering back to high school math) that a perpendicular inelastic slope means price/quantity is dividing by 0, a slope of infinity.
Richard

bkballa

elasticity of supply = 0 implies slope = infinity

karoliukas

You’re saying the elasticity of supply=0 for inelastic supply and elastic supply? You said elasticity of supply=0 implies slope=infinity. I’m confused.
Richard

cv4cfa

Slope is equal to zero for a perfectly inelastic supply because if it is perfectly inelastic then the %Q does not change for a given % change in price.
So if % change in Q = zero, then your slope for elasticity is zero as well. (Remember, elasticity = % change quantity / % change price)