Question

Given the following supply and demand functions:

Qdx = 1,800 - 4 Px + 0.3 Py - 0.3 Pz + 0.006 I
Qsx = 450 + 16 Px - 7 W - 0.2 R

Income (I) = 4,200
Price of Y (Py) = 190
Price of Z (Pz) = 80
Wages (W) = 20
Rent (R) = 180

1. What is the equilibrium price?  

2. What is the equilibrium quantity?  

In reduced form the demand is Qdx = Do - b (Px)

3. What is the horizontal intercept value, 'Do'?  

4: What is the value of 'b'? (use a negative sign in your answer)  

In reduced form the supply is Qsx = f(Px); Qsx = So + g (Px)

Part 5: What is the horizontal intercept, 'So'?  

Part 6: What is the value of 'g'?  

Answer 1

Given

Qdx =1800-4Px+0.3Py-0.3Pz+0.006I
Put Py=190

Pz=80

I=4200

Qdx =1800-4Px+0.3*190-0.3*80+0.006*4200
Qdx=1858.20-4Px

Given

Qsx = 450+16Px-7W-0.2R

Put W = 20
R = 180

Qsx =450+16Px-7*20-0.2*180

Qsx=274+16Px

1)

In equilibrium, Put Qdx=Qsx

1858.20-4Px=274+16Px

20Px=(1858.20-274)

Px=(1858.20-274)/20=79.21

Equilibrium price=79.21

2)

Let us calculate Qdx and Qsx at P=79.21

Qdx=1858.20-4*79.21=1541.36

Qsx=274+16*79.21=1541.36

So, equilibrium quantity=1541.36

3)

Our demand function is

Qdx=1858.20-4Px

On comparing with Qdx = Do - b (Px), we can say that

Do=1858.20

4)

Our demand function is

Qdx=1858.20-4Px

On comparing with Qdx = Do - b (Px), we can say that

b=-4

5)

Our supply function is

Qsx=274+16Px

On comparing with Qsx = So + g (Px)

We get So=274

6)

Our supply function is

Qsx=274+16Px

On comparing with Qsx = So + g (Px)

We get g=16