Answer to Question #185328 in Macroeconomics for HASAN ALI KHAN

Question

Formulate the demand equations and estimate Qd for P=33 by using the following data:   

Price level Quantity Demand

38 200

36 500

34 800

32 900

30 1000

28 1400

Answer 1

The formula for demand equation:

$y-y1=m(x-x1)$

y is the dependent variable which is price

x is the independent variable which is the quantity demanded

m is the slope

$m=\frac{y2-y1}{x2-x1}$

Let us take two points from the given data:

$y1=P1=36$

$x1=Q1=500$

$y2=P2=32$

$x2=Q2=900$

$m=\frac{P2-P1}{Q2-Q1}$

$m=\frac{32-36}{900-500}$

$m=\frac{-4}{400}=-0.01$

A negative slope means the negative relationship between quantity demand and price

$P-P1=m(Q-Q1)$

$P-36=-0.01(Q-500)$

$P-36=-0.01Q+5$

 $P=41-0.01Q$ is the damand equition

When P=33,

$33=41-0.01Q$

$Q=\frac{33-41}{-0.01}$

$Q=800$

 

When price is 33, quantity demanded is 800 units.