Question

2) Supply and Demand/Demand Analysis

Suppose that your analyst estimates the demand equation for good X as given below:

?^x_d = 12 − ?? − 2?? + 1?? + ?

Good X sells for $1 per unit, good Y sells for $2 per unit, good Z sells for $1 per unit, and consumer income is $4.

a. Using the information provided by your analyst, please determine the demand equation. (Please use graphs to support your answer).

b. Please calculate the own price elasticity of demand for good X. Is the demand for good X elastic, inelastic, or unit elastic? (Please indicate where on your graph of the demand equation from part a, your calculation of own-price elasticity lies.)

c. If I increase the price of good X by 0.13%, what happens to revenues? (Please use graphs to support your answer.)

Answer 1

Qx = 12 - Px - 2Py + Pz + M

Px = 1

Py = 2

Pz = 1

M = 4

a) Demand equation illustrate the relationship between price and quantity consumed of a good.

Qx = 12 - Px - 2 * 2 + 1 + 4

Qx = 13 - Px

b) Price elasticity of demand is calculated as [(dQ / dP) * (P / Q)]

dQ / dP is derivative of demand equation with respect to price = -1

Elasticity would be: -1 * [P / (13 - P)]

Put value of Px = 1

Elasticity: -1 * [1 / (13 - 1)] = -0.083 (We can ignore the negative sign because there always exist a negative relationship between price and quantity consumed)

Elasticity of demand less than 1 is classified as inelastic demand.

Inelastic demand lies in lower portion of demand curve.

c)  If price of good X rises by 0.13%, there will be rise in total revenue of good X being an inelastic good because consumers cannot reduce the quantity demanded of inelastic good.