Question

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1. Given the demand function Q = 100 - 10P, where P corresponds to price, do the following:

1. Plot the respective demand function. Be sure to label your axes. For what price will Q = 0? When P = 0, what is Q?
2. Derive the expression for the own-price elasticity. Is the own-price elasticity constant along all points on the demand curve? What price range insures that the demand for Q is inelastic?
3. Derive the inverse demand function. That is, rewrite the demand function such that

Answer 1

a ....... Demand function, Q = 100 — 10P

When Q =0 then demand function 100—10P = 0 or 10P =100 or P =100/10 =10 (vertical intercept of the demand curve)

When P =0 then from demand function , Q =100—10×0 or Q= 100 ( horizontal intercept of the demand curve)

Now put the values in the graph.

b..... Given the demand function Q =100 —10P

differentiating both sides with respect to P

dQ/dP = d(100 —10P)/dP = —10

Now price elasticity of demand (ep)=(dQ/dP)×(P/Q)

or, ep = (—10) ×(P/100—10P) put value of Q

or ep =(—10)×{P/10(10—P)} =—P/(10—P)

ep =P/(P—10) This is the required expression of price elasticity of demand for the given demand function.

No the own price elasticity of demand is not constant it is different for the different value of P

Demand will be price inelastic ep = P/(P—10) <1 if the price range is 0>=P< 5

c..........

demand function , Q = 100 — 10P

its inverse demand function will be

10P =100 —Q or P = (100—Q)/10

or P =10 —0.1P answer