Question

a demand curve is a straight line sloping downwards at an angle of 45 degrees.we can conclude that its price elasticity is a-1.0 b-0.5 c-constant d-variable

Answer 1

Answer: d - variable

When a demand curve is a straight line sloping downwards at an angle of 45 degrees, the value of its vertical and horizontal intercepts are same.

Tan =Perpendicular / Base

We know that Tan 45^o = 1

or, Perpendicular / Base = 1

Perpendicular = Base

In the above graph, price(P) is measured on the vertical axis, and quantity(Q) is measured on the horizontal axis. Let the maximum price is $30. So its corresponding maximum quantity would also be 30 unit. Joining maximum price, and maximum quantity, we get the downward sloping straight line demand curve, 'D₁D₁', which makes 45^o angle to the horizontal axis.

Price elasticity of demand(e) = - [(dQ/Q) / dP/P)]

Or, e = - (dQ/ dP) * (P/Q), [where, dQ/ dP = slope of the inverse demand curve]

Taking modulus of e, i.e., |e| = (dQ/ dP) * (P/Q)

Now, slope of the inverse demand curve = 1/(dP/dQ) = 1 / 1 = 1 [ dP/ dQ = 1]

When price is half of maximum price, i.e., when P = 15, we see its corresponding quantity is also 15.

So at the mid-point on the demand curve, the elasticity, e or |e| = (dQ/ dP) * (P/Q) = 1*1 = 1 = Unitary elasticity

Any point above the mid-point of the demand curve , |e| 1 , as PQ [Price rises, quantity demand decreases.]

Any point below the mid-point of the demand curve , |e| 1 , as PQ [Price decreases, quantity demand rises]

The two extreme points on the demand curve, are point 'T', and point 'L'.

At point T; |e| = ∞(infinity).

At point L; |e| = 0.

The value of price elasticity of demand for normal good is negative. To make the sign positive, we take the modulus of elasticity (e) , i.e., |e|.

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