The Demand Function and Elasticities
1. Suppose using household information we can estimate the following demand function:
Qx = 60- 5Px + 2.4 Py – 4Pz + 10I
where Qx = is the quantity of raincoats demanded during a one-year period measured in thousands of units, Px = the price of a rain coat, Py= price of a jacket, Pz represents the price of an umbrella, and I is the average annual income of prospective buyers, measured in thousands of dollars.
Further, based on current information, we have the following values for prices and income:
Px = $60, Py= $50, Pz = $20, and I = $40.
a) Use the given values (above) for other prices (except for the price of raincoat) and income
to calculate the following demand equation for raincoat using this format:
Qx = A + ο’1Px (Use the information to get the value for A and ο’1).
b) At the current price for the raincoat, how many raincoats will be demanded
c) Use the formula for point elasticity [(ο₯ = (dQ/dP) x (P/Q)] and the information you have from above to calculate the point elasticity of demand, what does it tell you?
d) Use the same information to calculate the Line (Arc) elasticity ο₯arc = [(Q1 – Q2)/(P1 – P2]) x [(P1 + P2)/(Q1 + Q2)].
e) Use the Point elasticity formula: ο₯I = (οQd/οI) (I/Qd) to calculate the income elasticity,
what does it tell you?
f) Use the Point elasticity formulas: ο₯xy = (οQx /οPy) (Py/Qx) and ο₯xz= (οQx /οPz) (Pz/Qx) to
to calculate the cross-price elasticity for jacket and umbrella, what does it tell you?
g) Using the information in (a), can you indicate how price change can impact the revenue?
