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Posted: May 22nd, 2024
The Demand Function and Elasticities
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 + 1Px (Use the information to get the value for A and 1).
b) At the current price for the raincoat, how many raincoats will be demanded
c) Use the formula for point elasticity [( = (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 arc = [(Q1 – Q2)/(P1 – P2]) x [(P1 + P2)/(Q1 + Q2)].
e) Use the Point elasticity formula: I = (Qd/I) (I/Qd) to calculate the income elasticity,
what does it tell you?
f) Use the Point elasticity formulas: xy = (Qx /Py) (Py/Qx) and xz= (Qx /Pz) (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?
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