Answer to Question #254997 in Microeconomics for bibble

Question

The demand function for Product X is given by:

Qdx = 10 + 0.06I - 2Px - 0.5Py + 0.7Pz

where

Px Price of good X $9.00

Py Price of related good Y $4.00

Pz Price of related good Z $10.00

I Income $250.00

a. (i) Calculate the own Price elasticity of demand (PED) for Good X.

(ii) Illustrate on a well labelled demand curve graph for Product X, the Total Revenue

earned when the Price of good X is equal to $9.00. This graph should be labeled

‘Graph 1: Total Revenue of Product X at price $9.00.’

(iii) Illustrate on another well labelled diagram, the area of Consumer surplus for Product X

when the price of good X is $9.00. This graph should be entitled ‘Graph 2: Consumer

Surplus of Product X.’

(iv) What is the value of the consumer surplus?

Answer 1

a. (i) find QDx:

$Qdx = 10 + 0.06I - 2Px - 0.5Py + 0.7Pz=10+0.06\times 250 000-2\times9-0.5\times4+0.7\times10=14997$

Px Price of good X $9.00

Py Price of related good Y $4.00

Pz Price of related good Z $10.00

I Income $250.00

$ЕРХ = \frac{dQDХ}{dРХ}\times\frac{РХ}{ QDХ} =\frac {-2\times 9}{14997}=0.0012$

(ii), (iii)

Total Revenue earned

$9\times14997=134973$

Q=15015-2P

(iv)let's say the price has dropped from 9 to 2

$Qdx = 10 + 0.06I - 2Px - 0.5Py + 0.7Pz=10+0.06\times 250 000-2\times2-0.5\times4+0.7\times10=15011$

consumer surplus:

$9\times14997-2\times15011=104951$