The price of beef in the United States has been found to depend on the demand (measured by per capita consumption) according to the equation q=342.5/p^0.5314 Find the elasticity. Is the demand for beef elastic or inelastic?

Answer 1

Q = 342.5 / P^.5314
dQ/dP = -342.5 (.5314) P^-.4686/ P^1.063
so
dQ/dP = - 182 P^-1.5316

well, we need to know what P is at the intersection P = q
P^1.5314 = 342.5
1.5314 log P = 2.535
log P = 1.655
P = 45.2
so dQ/dP at intersection = -182(45.2)^-1.5316
= .531

Answer 2

change in percent bought is only half the percent change in price