Demand Elasticity Reviewing arc elasticity A review problem

Demand Elasticity

Reviewing arc elasticity

A review problem with arc elasticity.

Point Elasticity = (d. Q/d. P) x (P/Q) Review Perfectly inelastic demand, Perfectly elastic demand.

Unitary price elasticity

Price elasticity and total revenue and marginal revenue

Price elasticity changes along a curve.

Empirical price elasticities.

Price elasticities by degree of luxury on an airline.

Elasticity is important for cigarette policy.

So, how elastic is the demand of cigarette buyers? The news item states the Surgeon General’s report that this demand elasticity in absolute value is between 0. 3 and 0. 5.

Increasing the Michigan price of cigarettes approximately $3. 50 to $4. 25 is a nearly 25% increase. To calculate the implied reduction in MI smoking, multiple the 25% times the elasticity estimate (0. 3 to 0. 5). That is, a 7. 5% to a 12. 5% reduction.

On the tax revenue side: Tax revenue is quantity change times tax change. So, the change in tax revenue is likely to be: A (1. 00 -. 075) x Q x $0. 75 to (1. 00 -. 125) x Q x $0. 75 increase.

Granholm’s administration estimates that this will amount to a $30, 000 gain in tax revenue for the state, and 150, 000 fewer smokers in Michigan. Because the cigarette elasticity for teenagers is larger, Granholm estimates that 94, 000 (fewer? ) teens will take up smoking in the state. Freep 2/10/04

A useful formula involving price elasticity states that MR = P(1 + 1/ ) Proven this way: We know that d(PQ)/d. Q = (d. P/d. Q)Q + P MR So, MR = (P/P)[(d. P/d. Q)Q + P] = P[d. P/d. Q)Q/P + 1] = P(1 + 1/ )

Income elasticity: n. Y = (d. Q/d. Y) x (Y/Q)

Income elasticity empirically.

Cross Price Elasticity XY = (d. Qx/d. Py)x(Py/Qx)

Revenue effect when demand is inelastic.