Logo

AskSia

Plus

1. Explain why demand curves that are linear (straight lines) generally do not ...
Oct 30, 2024
1 Solution
a
Demand Curve Elasticity: Linear demand curves are generally not constant in elasticity because elasticity varies along the curve. Elasticity is defined as Ed=ΔQ/QΔP/P E_d = \frac{\Delta Q / Q}{\Delta P / P} , which changes as price and quantity change
b
Constant Elasticity: A linear demand curve has constant elasticity only if it is a special case, such as a perfectly elastic demand curve (horizontal) or a perfectly inelastic demand curve (vertical)
Answer
Demand curves are not constant in elasticity except in special cases.
Key Concept
Elasticity of demand varies along linear demand curves except in special cases.
Explanation
Linear demand curves typically show changing elasticity, while perfectly elastic or inelastic curves maintain constant elasticity.
2 Solution
a
Demand Shock and Supply Curve: The effect of a demand shock varies with the supply curve's shape. A horizontal supply curve indicates perfectly elastic supply, leading to a large quantity change with a small price change
b
Supply Curve Shapes: A linear upward sloping supply curve results in moderate price and quantity changes, while a linear downward sloping curve indicates a decrease in quantity with price increases. A vertical supply curve shows no change in quantity regardless of price changes
Answer
The effect of a demand shock depends on the supply curve's elasticity.
Key Concept
The shape of the supply curve influences the impact of demand shocks.
Explanation
Different supply curve shapes lead to varying responses in price and quantity when demand shifts.
3 Solution
a
Elasticity Calculation: The demand equation is Q=200−10p Q = 200 - 10p . To find elasticity at p=10 p = 10 , first calculate Q Q : Q=200−10(10)=100 Q = 200 - 10(10) = 100 . Then, use the formula Ed=dQdP⋅PQ E_d = \frac{dQ}{dP} \cdot \frac{P}{Q} . Here, dQdP=−10 \frac{dQ}{dP} = -10 , so Ed=−10⋅10100=−1 E_d = -10 \cdot \frac{10}{100} = -1
Answer
The elasticity of demand at p=10 p = 10 is -1.
Key Concept
Elasticity of demand measures responsiveness to price changes.
Explanation
At p=10 p = 10 , the demand is unit elastic, indicating proportional responsiveness to price changes.
4 Solution
a
Elasticity of Supply Calculation: The formula for elasticity of supply is Es=ΔQ/QΔP/P E_s = \frac{\Delta Q / Q}{\Delta P / P} . Here, ΔP=0.80−0.60=0.20 \Delta P = 0.80 - 0.60 = 0.20 and ΔQ=100−50=50 \Delta Q = 100 - 50 = 50 . The average price P=0.60+0.802=0.70 P = \frac{0.60 + 0.80}{2} = 0.70 and average quantity Q=50+1002=75 Q = \frac{50 + 100}{2} = 75 . Thus, Es=50/750.20/0.70=2/32/7=73≈2.33 E_s = \frac{50/75}{0.20/0.70} = \frac{2/3}{2/7} = \frac{7}{3} \approx 2.33
Answer
The elasticity of supply is approximately 2.33.
Key Concept
Elasticity of supply measures how quantity supplied responds to price changes.
Explanation
A value greater than 1 indicates that supply is elastic, meaning quantity supplied is responsive to price changes.
5 Solution
a
Price Elasticity of Demand: The demand equation is Q=1000−5p+10pX−2pZ+0.1Y Q = 1000 - 5p + 10p_X - 2p_Z + 0.1Y . At p=80,pX=50,pZ=150,Y=20000 p = 80, p_X = 50, p_Z = 150, Y = 20000 , calculate Q Q : Q=1000−5(80)+10(50)−2(150)+0.1(20000)=1000−400+500−300+2000=2800 Q = 1000 - 5(80) + 10(50) - 2(150) + 0.1(20000) = 1000 - 400 + 500 - 300 + 2000 = 2800 . Then, Ed=dQdP⋅PQ E_d = \frac{dQ}{dP} \cdot \frac{P}{Q} where dQdP=−5 \frac{dQ}{dP} = -5 , so Ed=−5⋅802800=−1.14 E_d = -5 \cdot \frac{80}{2800} = -1.14
b
Cross-Price Elasticity with respect to Commodity X: The cross-price elasticity is EdX=dQdpX⋅pXQ E_{dX} = \frac{dQ}{dp_X} \cdot \frac{p_X}{Q} . Here, dQdpX=10 \frac{dQ}{dp_X} = 10 , so EdX=10⋅502800=0.18 E_{dX} = 10 \cdot \frac{50}{2800} = 0.18 . An example of commodity X could be a printer cartridge
c
Cross-Price Elasticity with respect to Commodity Z: Similarly, EdZ=dQdpZ⋅pZQ E_{dZ} = \frac{dQ}{dp_Z} \cdot \frac{p_Z}{Q} where dQdpZ=−2 \frac{dQ}{dp_Z} = -2 , so EdZ=−2⋅1502800=−0.11 E_{dZ} = -2 \cdot \frac{150}{2800} = -0.11 . An example of commodity Z could be a laser printer
d
Income Elasticity: The income elasticity is EY=dQdY⋅YQ E_Y = \frac{dQ}{dY} \cdot \frac{Y}{Q} where dQdY=0.1 \frac{dQ}{dY} = 0.1 , so EY=0.1⋅200002800=0.71 E_Y = 0.1 \cdot \frac{20000}{2800} = 0.71
Answer
a) Price elasticity of demand is approximately -1.14; b) Cross-price elasticity with respect to X is 0.18; c) Cross-price elasticity with respect to Z is -0.11; d) Income elasticity is 0.71.
Key Concept
Elasticities measure responsiveness of demand to price and income changes.
Explanation
Different elasticities indicate how demand reacts to changes in price of related goods and income levels.
6 Solution
a
Income Elasticity Calculation: The demand equation is Q=100−5p+2Y Q = 100 - 5p + 2Y . At p=4 p = 4 and Y=10 Y = 10 , Q=100−5(4)+2(10)=100−20+20=100 Q = 100 - 5(4) + 2(10) = 100 - 20 + 20 = 100 . The income elasticity is EY=dQdY⋅YQ E_Y = \frac{dQ}{dY} \cdot \frac{Y}{Q} where dQdY=2 \frac{dQ}{dY} = 2 , so EY=2⋅10100=0.2 E_Y = 2 \cdot \frac{10}{100} = 0.2
b
New Demand Equation: When income is measured in dollars, Y^=Y×1000 \hat{Y} = Y \times 1000 . The new demand equation becomes Q=100−5p+2Y^/1000 Q = 100 - 5p + 2\hat{Y}/1000 . At p=4 p = 4 , Y^=10000 \hat{Y} = 10000 , Q=100−20+20=100 Q = 100 - 20 + 20 = 100 . The income elasticity remains EY=0.2 E_Y = 0.2
c
Income Elasticity at Price 2: If the price falls to 2 2 , Q=100−5(2)+2(10)=100−10+20=110 Q = 100 - 5(2) + 2(10) = 100 - 10 + 20 = 110 . The income elasticity is EY=2⋅10110≈0.18 E_Y = 2 \cdot \frac{10}{110} \approx 0.18
Answer
a) Income elasticity is 0.2; b) New demand equation remains the same with quantity demanded at 100; c) Income elasticity at price 2 is approximately 0.18.
Key Concept
Income elasticity measures how demand changes with income variations.
Explanation
Income elasticity values indicate the responsiveness of demand to changes in consumer income.
7 Solution
a
Tax Incidence: The incidence of a tax can be analyzed by shifting the supply curve (tax on sellers) or the demand curve (tax on buyers). In both cases, the equilibrium price increases, and the quantity decreases
b
Equal Tax Incidence: The incidence of the tax is split equally between buyers and sellers when the price elasticity of demand equals the price elasticity of supply. This means both parties are equally responsive to price changes
Answer
Tax incidence can be shown as a shift in either supply or demand, and is split equally when elasticities are equal.
Key Concept
Tax incidence analysis shows how tax burdens are shared between buyers and sellers.
Explanation
The distribution of tax burden depends on the relative elasticities of demand and supply.
© 2023 AskSia.AI all rights reserved