Q8. 聽In Example 2.8 we examined the... [FREE SOLUTION]

Chapter 2: Q8. (page 85)

In Example 2.8 we examined the effect of a 20-percent decline in copper demand on the price of copper, using the linear supply and demand curves developed in Section 2.6. Suppose the long-run price elasticity of copper demand were -0.75 instead of -0.5.
Assuming, as before, that the equilibrium price and quantity are P_ = $3 per pound and Q_ = 18 million metric tons per year, derive the linear demand curve consistent with the smaller elasticity.
Using this demand curve, recalculate the effect of a 55-percent decline in copper demand on the price of copper.

Short Answer

Expert verified

The demand curve will be Q = 31.5 鈥� 4.5P.
The demand falls by 55% then price fall by 30%.

Step by step solution

Explanation for part (a)

Let the demand curve be Q = a + bP. The coefficient of P is the change in quantity demand by a change in price; the value of a is the intercept of the demand curve.

The elasticity of demand will be:

$E_{D} = \frac{鈻� Q}{鈻� P} 脳 \frac{P}{Q} E_{D} = - 0.75 - 0.75 = \frac{鈻� Q}{鈻� P} 脳 \frac{3}{18} \frac{鈻� Q}{鈻� P} = \frac{- 0.75 脳 18}{3} b = - 4.5$

The intercept value is calculated below:

18 = a - 4.5(3)

a = 18 + 13.5

a = 30.5

The demand curve will be Q = 31.5 鈥� 4.5P.

Explanation for part (b)

The demand curve falls by 55%; thus, the new demand curve will be:

$Q_{D}^{'} = 0.45 Q_{D} = 0.45 (31.5 - 4.5 P) = 14.18 - 2.03 P The supply curve is Q = - 9 + 9 P At equilibrium, D = S 14.18 - 2.03 P = - 9 + 9 P 2.03 P + 9 P = 14.18 + 9 11.03 P = 23.18 P = 2.10$