"Two years ago, jeans were priced at 72 dollars and 121,000 units were sold. Last year, the price was lowered to 68 and sales increased to 132,000. 1. Estimate the value of the demand elasticity...

"Two years ago, jeans were priced at 72 dollars and 121,000 units were sold. Last year, the price was lowered to 68 and sales increased to 132,000.

1. Estimate the value of the demand elasticity `e`?

My solution:  = `(132000-121000)/121000/(68-72)/72=-1.636`

2. based on your estimate of the demand elasticity , how many units would you expect to be sold if price were lowered by an additional dollar.

My question: Do I use the data (121,000 ; 72) and (q,67) to calculate this or the data (132,000 ; 68) and (q,67)?

I would think the first set of data, because in a) we calculate the price elasticity at the point (121,000 ; 72), but I am not sure. Can someone help me?

 

Expert Answers
pnrjulius eNotes educator| Certified Educator

In a sense we use both. I think what may be tripping you up is that normally when we estimate elasticities, we don't use the starting or ending point as the baseline; we use the midpoint as the baseline.

So instead of
((q2-q1)/q1)/((p2-p1)/p1)
as you did, we'd use the averages of q and p:
((q2-q1)/((q1+q2)/2))/((p2-p1)/((p1+p2)/2))
The 2s cancel out, so we have:
((q2-q1)/(q1+q2))/((p2-p1)/(p1+p2))

So  instead of what you had, we would do this:
e = ((132000-121000)/(132000 +121000))/((68-72)/(68+72)) = (11000/253000)/(-4/140) = (0.043478)/(-0.0285714) = -1.522

Now it asks for what would happen if we drop the price an additional dollar, so we should start with where we currently are, which is (132000, $68).

Generally we'd assume that our elasticity is constant, so we simply need to know what the percentage change in p is, which we then multiply by the elasticity to get the percentage change in q.

Dropping the price $1 from $68 to $67 is a change of -1.47%.
Thus, the quantity will change by (-0.0147)(-1.522) = 0.0224
The quantity sold will therefore increase by 2.24%.

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