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Question 1: Consider a good that has an existing demand curve given by Q = 44 – 6p and an existing
supply curve given by Q = 12 + 2p. Suppose there is a change in the demand curve and the new
demand curve is given by Q = 32 – 8p. There is no change in the supply curve.
a) Is the new demand curve a parallel shift from the existing demand curve? Briefly explain your answer.
b) Does the new demand curve lie on the right or left of the existing demand curve? Briefly explain your answer.
c) Determine the existing equilibrium price and quantity before the change in the demand curve.
d) Determine the new equilibrium price and quantity after the change in the demand curve.

Respuesta :

The demand and supply curve give the quantity demanded and supplied at a given price

  • a) The new demand curve is not parallel to the existing demand curve
  • b) The new demand curve lay on the left of the existing demand curve
  • c) Before the change in the demand curve, the equilibrium price is 4 and the equilibrium quantity is 20
  • d) After the change in the demand curve, the equilibrium price is 2 and the equilibrium quantity is 16

Reason:

Question 1:

Existing demand curve function is Q[tex]_d[/tex] = 44 - 6·p

Existing supply curve function is Q[tex]_s[/tex]  = 12 + 2·p

New demand curve function is Q[tex]_{new \, d}[/tex] = 32 - 8·p

No change in supply curve

a) The slope of the demand curve is given by the coefficient of p

Two demand curves are parallel if their slopes are equal or the same

The coefficient of p, of the existing demand curve, (-6) is not the same as the coefficient of p, in the new demand curve, (-8), therefore, the slopes are different, and the new demand curve is not parallel to the old demand curve

b) The y-value of the y-intercept of the existing demand curve is 44

The y-value of the y-intercept of the new demand curve is 32

The x-value of the x-intercept of the existing demand curve is [tex]p = \frac{44}{6} = 7.\overline 3[/tex]

x-value of the x-intercept of the new demand curve is [tex]p = \frac{32}{8} = 4[/tex]

The y, and x-intercepts of the new demand curve are lower than those of the existing demand curve, therefore;

  • The new demand curve lie on the left of the existing demand curve

c) The equilibrium price before the change  in the demand curve is given by the solution of the existing demand and supply curve as follows;

At equilibrium, we have;

Q[tex]_d[/tex] = Q[tex]_s[/tex]

Therefore;

44 - 6·p = 12 + 2·p

44 - 12 = 2·p + 6·p

32 = 8·p

[tex]p = \dfrac{32}{8} = 4[/tex]

The equilibrium price, p = 4

The equilibrium quantity is 44 - 6 × 4 = 12 + 2 × 4 = 20

The equilibrium quantity = 20

d)  The new equilibrium price is given as follows;

Q[tex]_s[/tex] = Q[tex]_{new \, d}[/tex]

We have;

12 + 2·p = 32 - 8·p

2·p + 8·p = 10·p = 32 - 12 = 20

[tex]p = \dfrac{20}{2} = 2[/tex]

p = 2

The equilibrium price, p = 2

The equilibrium quantity = 12 + 2× 2 = 16

Learn more here:

https://brainly.com/question/18426868

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