If the supply of a good decreases and it causes total revenue to increase, this shows that the good has an a) inelastic demand b) inelastic supply c) elastic supply d) unit elastic demand e) elastic demand

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Elasticity refers to the extent that demand or supply reacts to a change in price. If the supply/demand is responsive to a price change, that is small changes in price greatly affect the supply/demand, then it is elastic. Conversely, if supply/demand is unresponsive, it is considered inelastic, meaning a great...

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Elasticity refers to the extent that demand or supply reacts to a change in price. If the supply/demand is responsive to a price change, that is small changes in price greatly affect the supply/demand, then it is elastic. Conversely, if supply/demand is unresponsive, it is considered inelastic, meaning a great change in price is required to affect supply/demand. Unitary elasticity means a change in price causes an equal change in supply/demand.

Elasticity = (% change in quantity / % change in price)

If the above equation yields a number

> 1, the curve is elastic

= 1, the curve is unitary

< 1, the curve is inelastic

What we are looking at is the relationship between supply and demand. In your question, the supply is increasing, so we need to know how this relates to the demand, leaving us with possible answers a, d, or e.

We can use the Midpoint Method for finding elasticity by using the following formula:

**See attached photo 1**

Where Q is the quantity and P is the income/price.

Also, since we have 100 on both the top and bottom, we will cancel these out.

Although we do not have actual numbers in this question, we can still come up with some to illustrate the concept. Since our supply decreased, let’s say our previous (before) supply was 100 and our current (after) is 75. Since our income increased, let’s say our previous price was $3.00 and our current price is $5.00. Plug these into the equation:

**See attached photo 2**

We can drop the negative sign because elasticity is always negative. Now, applying what we learned above, 0.58 < 1, so the curve is inelastic.

Out of our remaining possible answers, this leaves us with a) inelastic demand.

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We are shifting the supply curve, which means we're moving along the demand curve--so the elasticity we're interested in is the elasticity of demand, which narrows it down to (a), (d), or (e).

By decreasing supply, we increase revenue. This means that as quantity sold Q goes down, the price P rises so much that the revenue P*Q goes up.

In terms of math, this means that the rate of change in [P*Q] with respect to Q is negative:

d[PQ]/dQ < 0

Using the Chain Rule we can separate this into two parts:

P + dP/dQ * Q < 0

With some simple algebra, we can turn this into an expression of the inverse elasticity:

dP/dQ * Q < - P

dP/dQ * Q/P < -1

The elasticity is just the inverse of this, and yes, indeed, dP/dQ = 1/(dQ/dP), though this is actually a calculus theorem and not nearly as obvious as it looks at first.

Also, don't forget to reverse the inequality when you take the reciprocal of both sides:

dQ/dP * P/Q > -1

That is, demand is inelastic, because an elasticity greater than -1 means an elasticity closer to 0. Therefore the answer is (a), inelastic demand.

In words, what we're saying is that we only have to decrease the quantity sold a little bit to get the price to rise a lot, and that means quantity is falling slower than price is rising, so demand must be inelastic.

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