Question

The supply function is Q 60 2p - 20r, and the demand function is Q- 260-2p, where r is the rental cost of capital. How do the equilibrium price and quantity vary with r? The effect of r on the equilibrium price is (Enter your resonse as a whole number.) The effect of r on the equilibrium quantity isEnter your resonse as a whole number.) op

Answer 1

According to the question,

The equilibrium in the market will be at the point where quantity demanded is equal to quantity supplied.

Given :

Q_d = 80+2p-20r

Q_s= 260-2p

Q_d =  Q_s

80+2p-20r = 260-2p

Reaaranging the terms,

2p+2p = 260-80+20r

4p = 180+20r

Taking 4 common in above equation, we get

p = 45 +5r

Using equation of p in equations Qd or Qs to get equilibrium quantity:

Qe = 80+2*(45 +5r)-20r

Qe= 80+90+10r-20r

Equilibrium Q = 170-10r

Similarly,

Q_e = 260-2*(45 +5r)

Q_e = 260-90-10r

Q_e = 170-10r

Equilibrium price : p = 45 +5r

Equilibrium Quantity: Q = 170-10r

The equilibrium price increases with r as shown in the table below and also the effect of r on equilibrium price is positive (5>0). However, the equilibrium quantity decreases with r as shown in the table below and also the effect of r on equilibrium quantity is negative (-10<0).

	r=0	r=1	r=2	r=3	r=4	r=5
p = 45 +5r	45	50	55	60	65	70
Q = 170-10r	170	160	150	140	130	120

The effect of r on equilibrium price is

p = 45 +5r

Differentiating p with respect to r:

$\frac{dp}{dr} = 5$

The effect of r on equilibrium Quantity is

Q = 170-10r

Differentiating Q with respect to r:

$\frac{dQ}{dr} = -10$