Answer to Question #274182 in Microeconomics for Arlind

Question

The market for commodity X is described by the following demand and supply curves.

                                         2

                  Q(p) = 25 – P   ………………(1)

                  Q(p) = -3 + 3P ………………(2)

(a)   Which of the two curves is the demand curve and which is the supply curve? How did you know?

(b)  Graph both curves (on the same graph)and find the equilibrium price and the equilibrium quantity transacted.

(c)   Solve algebraically for the equilibrium values in part (b).

(d)  Find the price elasticity of demand at equilibrium and interpret your result.

Answer 1

a)

Demand curve equation is $Q(p) = 25 – P ………………(1)$ since demand is negatively related to price.

Supply curve equation is $Q(p) = -3 + 3P ………………(2)$ since supply is positively related to price.

b)

$Q = 25 -P\\ When \ P =0$ , Q=25

$=> Q =25 -0 => Q = 25$

Vertical axis intercept for the demand curve.

$Q=25 -P$

Put $Q=0$ and calculate P

$=> 0 = 25 -P => P = 25$

For the supply curve vertical intercept is:

$Q=-3 + 3P$

Put $Q=0$ and calculate for P

$=> 0 =-3 + 3P => 3 = 3P$

$=> P =\frac{3}{ 3} => P =1$

At the equilibrium, the demand curve and the supply curve cross each other.

Therefore, the equilibrium quantity is 18 and equilibrium price is 1.

c)

Demand = supply at the equilibrium.

$=> 25 -P = -3 + 3P\\ =>3P + P= 25 + 3 \\ => 4P+ 28 =>P =\frac{28}{4}$

$=> P = 7 \\ and\\ Q = 25 - P\\ => Q = 25 -7\\ => Q = 18$

Therefore, equilibrium quantity is 18 and equilibrium price 7

d)

Price elasticity of demand:

$Ed = \frac{dQ}{dP}\times \frac{P}{Q}$

$Q = 25 - P$

$=>\frac{ dQ}{ dP} = -1$

$P=7\\ Q = 18$

$=> Ed =-1\times\frac{7}{ 18}$

$=>Ed = -0.388$

The absolute value of ED = 0.388. The demand is inelastic as the value is negative.