Question

1. suppy curve PQ=4
(1) P=4, Q=?, TR=?, the price elascity=?
(2) P=3 Q=?, TR=?, the prics elascity=?

2. suppy curve P=4/root(Q)
(1) P=4, Q=?, TR=? The price elascity=?
(2) P=3 Q=?, TR=? The price elascity=?

I want detailed explanation, thank you very much??

Answer 1

Solution

(1)

(Supply curve )PQ= 4 or P=4/Q

here P=4

so 4Q=4

Q=1

and Total revenue(TR) =P*Q

TR=4

Elasticity (e)=(ΔQ/ΔP)⋅(P\Q)

here

Q=4/P

ΔQ/ΔP=-4/P²

and P=4

So

ΔQ/ΔP=-4/4²

ΔQ/ΔP=-1/4

so

e=(-1/4)(4/1)

e=-1

(2)

here P=3

3Q=4

so Q=4/3

Total revenue(TR) =P*Q

TR=4

Elasticity (e)=(ΔQ/ΔP)⋅(P\Q)

here

Q=4/P

ΔQ/ΔP=-4/P²

and P=3

So

ΔQ/ΔP=-4/3²

ΔQ/ΔP=-4/9

so

e=(-4/9)(3*3/4)

e=-1

(3) P=4/√ Q or   

√Q=4/P

Q=16/P² inverse demand function

here

P=4

so

4=4/√ Q

√ Q=4/4

√ Q=1

Q=1

and Total revenue(TR) =P*Q

TR=4*1

TR=4

Elasticity (e)=(ΔQ/ΔP)⋅(P\Q)

here

Q=16/P²

ΔQ/ΔP=-2(16/P³)

ΔQ/ΔP=-32/P³

and P=4

So

ΔQ/ΔP=-32/4³

ΔQ/ΔP=-1/2

so

e=(-1/2)(4/1)

e=-2

(4)

P=4/√ Q or   

√Q=4/P

Q=16/P² inverse demand function

here

P=3

so

3=4/√ Q

√ Q=4/3

Q=16/9

and Total revenue(TR) =P*Q

TR=3*(16/9)

TR=16/3

Elasticity (e)=(ΔQ/ΔP)⋅(P\Q)

here

Q=16/P²

ΔQ/ΔP=-2(16/P³)

ΔQ/ΔP=-32/P³

and P=4

So

ΔQ/ΔP=-32/4³

ΔQ/ΔP=-1/2

so

e=(-1/2)(3*9/16)

e=-27/32

e=-0.84