Problen Set 3
Travis Kellenberger
AGEC 700
Problem Set #3
2) 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 firm's revenue if it decided to charge a price below $140?
At the given prices, quantity demanded is 750 units: Qdx = 1,200- (3 *140) -.1 (300) = 750.
-140/750=-.56; demand is inelastic at this price point and you would be decreasing total revenue with anything under
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 firm's revenue if it decided to charge a price above $240?
At the given prices, quantity demanded is 483 units: Qdx = 1,200- (3 *240) +.1(300) = 450.
-3 240/750=-1.6; demand is elastic at this price point and you would be decreasing total revenue if the firm increased the price
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 compliments?
Quantity demanded is 750 units. .01 300/750 = -.04. Negative number = goods X & Z are compliments
4) Suppose the own price elasticity of demand for good X is -3, its income elasticity is 1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Y is -4. Determine how much the consumption of this good will change if: a) The price of good X increases by 5 percent Price elasticity of demand formula %∆Qdx/-5 =-3. Then Solving, we see that the quantity demanded of good X will increase by 15 percent if the price of good X decreases by 5 percent.
b) The price of good Y increases by 8 percent
Price elasticity of demand formula %∆Qdx/8 =-4. Then Solving, we see that the quantity demanded of good X will decrease by 32 percent if the price of good Y increases by 8 percent
c) Advertising decreases by 4 percent
Price elasticity of demand formula %∆Qdx/-4 =2.
AGEC 700
Problem Set #3
2) 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 firm's revenue if it decided to charge a price below $140?
At the given prices, quantity demanded is 750 units: Qdx = 1,200- (3 *140) -.1 (300) = 750.
-140/750=-.56; demand is inelastic at this price point and you would be decreasing total revenue with anything under
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 firm's revenue if it decided to charge a price above $240?
At the given prices, quantity demanded is 483 units: Qdx = 1,200- (3 *240) +.1(300) = 450.
-3 240/750=-1.6; demand is elastic at this price point and you would be decreasing total revenue if the firm increased the price
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 compliments?
Quantity demanded is 750 units. .01 300/750 = -.04. Negative number = goods X & Z are compliments
4) Suppose the own price elasticity of demand for good X is -3, its income elasticity is 1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Y is -4. Determine how much the consumption of this good will change if: a) The price of good X increases by 5 percent Price elasticity of demand formula %∆Qdx/-5 =-3. Then Solving, we see that the quantity demanded of good X will increase by 15 percent if the price of good X decreases by 5 percent.
b) The price of good Y increases by 8 percent
Price elasticity of demand formula %∆Qdx/8 =-4. Then Solving, we see that the quantity demanded of good X will decrease by 32 percent if the price of good Y increases by 8 percent
c) Advertising decreases by 4 percent
Price elasticity of demand formula %∆Qdx/-4 =2.