Question

"The demand for scooters is:  Q = 6000 – 40P + 0.05Y

Where Q is number of scooters, P is the Price, and Y is income."

a) Calculate the price elasticity of demand (arc elasticity) from P = $110 to P = $120, when Y = $50,000.

Enter as a value (ROUND TO TWO DECIMAL PLACES. ANSWER SHOULD BE A POSITIVE NUMBER.).

b) b) What happened to Total Revenue when P increased from $110 to $120?

Group of answer choices

Decreased

Increased

Stayed the same

c) Given your answers in part a and b, would you expect the price that maximizes Total Revenue to be:

Group of answer choices

Less than $110

Equal to $110

Greater than $110

d) When Y = $50,000, what Price maximizes Total Revenue?

e) Suppose there is a shortage of bicycles at stores. How would this affect the elasticity of demand for scooters?

Answer 1

a) 1.18
(At P1 = 110; Y = 50,000; Q1 = 6000 – 40P + 0.05Y = 6000 – 40(110) + 0.05(50,000) = 6000 - 4400 + 2500 = 4100
At P2 = 120; Y = 50,000; Q2 = 6000 – 40P + 0.05Y = 6000 – 40(120) + 0.05(50,000) = 6000 - 4800 + 2500 = 3700
E = )

b) Decreased
(As demand is elastic so TR decreased.)

c) Less than $110
(Demand will be inelastic at a lower price.)

d) 106.25
(Q = 6000 – 40P + 0.05Y = 6000 – 40(P) + 0.05(50,000) = 6000 - 40P + 2500 = 8500 - 40P
dQ/dP = -40
E = -1 = (dQ/dP)*(P/Q) = (-40)*P/(8500 - 40P)
So, 40P = 8500 - 40P
So, 40P + 40P = 80P = 8500
So, P = 8500/80 = 106.25)

e. It will become less elastic
(As bicycles are a substitutes so shortage of substitutes will make demand for scooters less elastic.)