Microeconomics, Module 11: "Monopoly" (Chapter 10) comments on the Illustrative Test Questions

In 11.2, for a competitive industry, doesn't the shortage cause an upward shift of $1 of the supply curve, causing a move of the short-run equilibrium 'up' the demand curve - a decrease in quantity and an increase in price of less than $1? 

What does it mean to say "A linear demand curve is elastic when quantity is small and inelastic when quantity is large." I thought the elasticity had to do with the slope of the demand curve? This doesn't change when quantity changes. What am I missing here?

yes, it's related to the slope of the demand curve, but also to the acual proportion of P/Q, which is different for different points on the demand curve.

[NEAS: Correct; see the Jacob / Rachel dialogue below.]

A belated reply to wayno52's first comment above: I think the NEAS posting is correct for 11.2 - in a competitive market, the price will rise by exactly $1 a pound. wayno52 is correct that the supply curve will shift up by exactly $1, but remember that the supply curve is the same as the marginal cost curve, and the marginal cost curve (we are told) is constant. So, when the horizontal supply curve shifts up by $1, the price correspondingly shifts up by $1. Quantity demanded should drop, but the price still goes up by exactly $1.

[NEAS: Correct.  This is true only for a constant marginal cost curve, as the problem assumes.]

Jacob: What does it mean that the elasticity varies over a linear curve but is constant over a logarithmic curve?

Rachel: The price elasticity of demand (η) = MQ/MP × P/Q.

For a linear demand curve, Q = α – ßP, so the elasticity (η) = MQ/MP × (P/Q) = –ßP / (α – ßP).

~ If P is near zero, the elasticity is close to zero.

~ If Q is near zero, α . ßP, so the elasticity is close to –4.

If the relation between two variables is multiplicative, or Y = α Z^β, we take logarithms of both sides to get ln(Y) = ln(α) + β ln(Z). This is a logarithmic curve.

β is the derivative of ln(Y) with respect to ln(Z).

Mln(Y) = MY/Y and Mln(Z) = MZ/Z.

Mln(Y) / Mln(Z) is the elasticity of Y with respect to Z.

 

The elasticity is constant over the curve.