Question

On the basis that the demand equation is linear, the demand curve must therefore be a straight. From microeconomic theory we know that the quantity q and price p are linearly related. Therefore, if we have data that tell us that when the value of p=58 the value of q=100 and when the value of p=51 the value of q= 200 we can say that these can be represented in a plane of coordinates q,p by points (100,58) and (200,51). Find the demand equation

Answer 1

Given data points:
(P1, Q1) = (58, 100)

(P2, Q2) = (51, 200)

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A straight line on the 2D plane is uniquely characterized by two features:

i ) Slope, or equivalently angle of inclination with the positive side of the X-axis
ii) Y-intercept, or the point at which the line intersects the Y-axis

So we can write the generic equation for a straight line:

y = mx + c; where m is the slope and c is the Y-intercept

and reframe the problem as finding m and c
since a unique pair (m, c) uniquely specifies a straight line on the 2D plane

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m (the slope) can be interpreted as the rate of change of the Y-axis variable with respect to the X-axis variable.

So m is given by

m = [(Magnitude of Change in Y variable) / (Magnitude of change in X variable)]
=> m = [ (p2 - p1) / (q2 - q1) ]
= [ ( 51 - 58 ) / ( 200 - 100 ) ]
= [ -7 / 100 ]
= -0.07

So the equation is y = (-0.07)x + c
OR, interpreting it back to economic terms, p = (-0.07)q + c
plug in any of the data points ( x, y) to find unknown c

58 = (-0.7)*100 + c
=> 58 = -7 + c => c = 65

[ Using the other data point would've given the same answer:
51 = (-0.07)*200 + c
=> 51 = -14 + c
=> c = 51 + 14 = 65]

ANswer: Equation for the demand curve is p = (-0.07)q + 65
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