The demand curve for a product is given by Qdx= 1,200 - 3Px + .01Pz where Pz = $
ID: 1178645 • Letter: T
Question
The demand curve for a product is given by Qdx= 1,200 - 3Px + .01Pz where Pz = $300.
a. What is the own price elasticity of demand when Px = $140? Is demand elastic or inelastic at this price? What would happen to the firms revenue if it decided to charge a price below $140?
b. What is the own price elasticity of demand when Px = $240? Is demand elastic or inelastic at this price? What would happen to the firms revenue if it decided to charge a price above $240?
c. What is the cross-price elasticity of demand between good X and good Z when
Px = $140? Are goods X and Z substitutes or complements?
Explanation / Answer
a. Since the price of Z is $300. The demand function is
Q = 1200 - 3P + 0.01(300)
Q = 1203 - 3P
From this we have, dQ/dP = -3
Find quantity at the given price of $140.
Q = 1203 - 3(140)
Q = 783
Now substitute the values in the own-price elasticity formula.
Ed = -(dQ/dP)(P/Q) = -(-3)(140/783) = 0.54
The demand is inelastic.
From the relationship between total revnue and elasticity, we know that, since demand is inelastic, firm's total revenue will fall if it decided to reduce its price.
b.
a. Since the price of Z is $300. The demand function is
Q = 1200 - 3P + 0.01(300)
Q = 1203 - 3P
From this we have, dQ/dP = -3
Find quantity at the given price of $240.
Q = 1203 - 3(240)
Q = 483
Now substitute the values in the own-price elasticity formula.
Ed = -(dQ/dP)(P/Q) = -(-3)(240/483) = 1.49
The demand is elastic.
From the relationship between total revnue and elasticity, we know that, since demand is elastic, firm's total revenue will fall if it decided to increase its price.
c.
From the given demand function, we have dQ/dPz = 0.01.
Find the quantity at the given prices.
Q = 1200 - 3(140) + 0.01(300) = 783
Now substitute the values in the cross-price elasticity formula.
E = (dQ/dPz)(Pz/Q) = (0.01)(300/783) = 0.0038
Since a rise in the price of Z causes a rise in the demand for X, the goods are substitutes.
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