Question

15. Suppose that budding economist Buck mea- sures the inverse demand curve for toffee as P $100 - and the inverse supply curve as P Buck's economist friend Penny likes to measure everything in cents. She measures the in- verse demand for toffee as P 10,000 100Q and the inverse supply curve as P- 100 0 a. Find the slope of the inverse demand curve, and compute the price elasticity of demand at the market equilibrium using Buck's measurements. b. Find the slope of the inverse demand curve, and compute the price elasticity of demand at the market equilibrium using Penny's measure- ments. Is the slope the same as Buck calculated? How about the price elasticity of demand?

Answer 1

a) Bucks measurements

For equllibrium price and quantity

Qd = Qs

Qs = P

Qd = 100-P ( from the equation P = 100-Qd)

100-P = P

100=2P

P = 50$

Equllibrium quantity = 100-P = 100-50 = 50

Inverse demand curve :

P = 100-Qd

P = 100+(-1)Qd which is in the form y = mx+c

m = slope = -1

Price elasticity of demand = (-1/m)(P/Q)

PED = (-1/-1)(50/50) = 1

b) Penny measurements

For equllibrium price and quantity

Qd = Qs

Qd = (10000-P)/100 = 100-0.01P

Qs = P/100 = 0.01P

(100- 0.01P)=0.01P

100=0.02P

P = 5000 cents

Q= 100-0.01P = 100-(0.01*5000)=50

Slope of inverse demand curve :

P = 10000-100Qd

Here slope as per y= mx+C

m = slope = -100

PED = (-1/m)(P/Q)

PED = (-1/-100)(5000/50) = 1

Slope is not same as Buck calculated as the value of price is measured in Buck case is dollar and in Penny case is per cents.

The PED is same in both the cases as the equllibrium price and quantity in both cases is same as 1 dollar = 100 cents

Which means 5000 cents = 50 dollars.