Question

1. Consider a straight-line demand curve which goes through the points (p=12, q=2200 )) and (p=10, q=2400).

a. Calculate arc elasticity

b. At each of the two points calculate point elasticity

c. Calculate point elasticity at a price of 12.

2. Consider the demand curve P = 300 - .6Q. Calculate the elasticity of demand at P = 200.

3. Consider a straight-line Engel’s curve which goes through the points (I=2000, q=2200) and (I=2200, q=2500).

a. Calculate point elasticity at an income of 2200.

b. What can you say about the type of the good?

Answer 1

a. To calculate the arc elasticity, we use the formula:

Arc Elasticity = ((q2 - q1) / ((q2 + q1) / 2)) / ((p2 - p1) / ((p2 + p1) / 2))

Given: (p1, q1) = (12, 2200) and (p2, q2) = (10, 2400)

Arc Elasticity = ((2400 - 2200) / ((2400 + 2200) / 2)) / ((10 - 12) / ((10 + 12) / 2))

Arc Elasticity = (200 / 2300) / (-2 / 11)

Arc Elasticity = -0.0869

b. Point elasticity is calculated using the formula:

Point Elasticity = (dq / q) / (dp / p)

At point (p=12, q=2200):

Point Elasticity = ((dq / q) / (dp / p)) = ((dq / 2200) / (-2 / 12)) = -3.6

At point (p=10, q=2400):

Point Elasticity = ((dq / q) / (dp / p)) = ((dq / 2400) / (2 / 10)) = 4.17

c. To calculate the point elasticity at a price of 12:

Point Elasticity = ((dq / q) / (dp / p)) = ((dq / 2200) / (0 / 12)) = undefined (as the denominator is zero)

Given demand curve: P = 300 - 0.6Q

To calculate the elasticity of demand at P = 200:

Elasticity of Demand = (dQ / Q) / (dP / P)

Here, dQ = -1 (change in quantity), Q = Q (original quantity),

dP = -100 (change in price), P = 200 (original price)

Elasticity of Demand = ((-1 / Q) / (-100 / 200)) = 2 / Q

a. To calculate the point elasticity at an income of 2200:

Point Elasticity = ((dq / q) / (dI / I))

Given: (I1, q1) = (2000, 2200) and (I2, q2) = (2200, 2500)

Point Elasticity = ((2500 - 2200) / 2500) / ((2200 - 2000) / ((2200 + 2000) / 2))

Point Elasticity = 0.3333

b. Based on the calculated point elasticity at an income of 2200, it suggests that the good is income inelastic, meaning that the quantity demanded does not significantly change with an increase in income.