Logo

AskSia

Plus

Questions 1. Hirschey et al. 16th 16^{\text {th }} Edition: Chapter 3, Q3.4. The E...
Aug 11, 2024
Solution by Steps
Question 1: Demand Function and Demand Curve
step 1
A demand function is a mathematical representation that shows the relationship between the quantity demanded and various factors, such as price, income, and prices of related goods. A demand curve, on the other hand, is a graphical representation of the demand function, typically showing the quantity demanded at different price levels
step 2
A movement along a demand curve occurs when there is a change in the price of the good itself, leading to a change in the quantity demanded. In contrast, a shift in the demand curve happens when there is a change in any other factor affecting demand (like income or prices of substitutes), resulting in a new demand curve
Answer
A demand function is a mathematical equation, while a demand curve is its graphical representation. Movements along the curve are due to price changes, while shifts are due to other factors.
--- Question 2A: Demand and Supply Functions
step 1
Substitute the given values PW=4 P_W = 4 , Y=15000 Y = 15000 , PL=8 P_L = 8 , and R=20 R = 20 into the demand function QD=−1450−25P+12.5PW+0.1Y Q_D = -1450 - 25P + 12.5P_W + 0.1Y
step 2
The demand function becomes QD=−1450−25P+12.5(4)+0.1(15000) Q_D = -1450 - 25P + 12.5(4) + 0.1(15000) . Simplifying gives QD=−1450−25P+50+1500=0−25P Q_D = -1450 - 25P + 50 + 1500 = 0 - 25P
step 3
For the supply function, substitute the same values into QS=−100+75P−25PW−12.5PL+10R Q_S = -100 + 75P - 25P_W - 12.5P_L + 10R
step 4
The supply function becomes QS=−100+75P−25(4)−12.5(8)+10(20) Q_S = -100 + 75P - 25(4) - 12.5(8) + 10(20) . Simplifying gives QS=−100+75P−100−100+200=75P−100 Q_S = -100 + 75P - 100 - 100 + 200 = 75P - 100
Answer
Demand function: QD=−25P Q_D = -25P ; Supply function: QS=75P−100 Q_S = 75P - 100
--- Question 2B: Surplus or Shortage Calculation
step 1
Calculate the quantity demanded and supplied at P=1.50 P = 1.50 : QD=−25(1.50)=−37.5 Q_D = -25(1.50) = -37.5 and QS=75(1.50)−100=12.5 Q_S = 75(1.50) - 100 = 12.5
step 2
At P=2 P = 2 : QD=−25(2)=−50 Q_D = -25(2) = -50 and QS=75(2)−100=50 Q_S = 75(2) - 100 = 50
step 3
At P=2.50 P = 2.50 : QD=−25(2.50)=−62.5 Q_D = -25(2.50) = -62.5 and QS=75(2.50)−100=87.5 Q_S = 75(2.50) - 100 = 87.5
step 4
Surplus or shortage is calculated as QS−QD Q_S - Q_D . For P=1.50 P = 1.50 , shortage of 12.5−(−37.5)=50 12.5 - (-37.5) = 50 . For P=2 P = 2 , surplus of 50−(−50)=100 50 - (-50) = 100 . For P=2.50 P = 2.50 , surplus of 87.5−(−62.5)=150 87.5 - (-62.5) = 150
Answer
At P=1.50 P = 1.50 : shortage of 50; at P=2 P = 2 : surplus of 100; at P=2.50 P = 2.50 : surplus of 150.
--- Question 2C: Market Equilibrium Price/Output Combination
step 1
Set the demand function equal to the supply function: −25P=75P−100 -25P = 75P - 100
step 2
Combine like terms: 100=100P 100 = 100P
step 3
Solve for P P : P=1 P = 1
step 4
Substitute P=1 P = 1 back into either function to find quantity: QD=−25(1)=−25 Q_D = -25(1) = -25 or QS=75(1)−100=−25 Q_S = 75(1) - 100 = -25
Answer
Market equilibrium price is P=1 P = 1 with quantity Q=−25 Q = -25 .
--- Question 3: Elasticity Statements
step 1
For statement A, since the price elasticity is -5 (elastic), a price reduction will increase the quantity demanded and total revenue. Thus, this statement is true
step 2
For statement B, the cross-price elasticity of -4 indicates that a 5% reduction in price will lead to a 20% increase in software demand, making this statement true
step 3
For statement C, the price elasticity of -5 indicates demand is elastic, and since the income elasticity is 2.5, personal computers are cyclical normal goods, making this statement true
step 4
For statement D, falling software prices will increase demand for computers (cross-price elasticity is negative), thus increasing revenues for both, making this statement true
step 5
For statement E, a 2% price reduction is necessary to offset a 1% decline in income, making this statement true
Answer
All statements A, B, C, D, and E are true.
---
Key Concept
Understanding demand functions, supply functions, and elasticity is crucial in economics.
Explanation
Demand and supply functions help determine market behavior, while elasticity measures responsiveness to price changes, influencing revenue and market dynamics.
© 2023 AskSia.AI all rights reserved