Economics Problems
The image appears to present a set of economics questions, primarily focusing on elasticity concepts. Let’s go through these questions one by one:
12. Price Elasticity of Demand
Question 12:
Bir ailenin, tavuk eti talebinin fiyat esnekliği (-2)'dir. Fiyatı 5 TL olan tavuk etinden almak istediği miktar ayda 5 kg olan bu aile, tavuk etinin kilosu kaç TL’ye çıkarsa ayda 2 kg tavuk eti talep eder?
Answer:
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Price Elasticity of Demand ((E_d)): This measures how the quantity demanded changes as the price changes. The elasticity given is (-2), indicating that a 1% increase in price results in a 2% decrease in quantity demanded.
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Formula: (E_d = \frac{% \Delta Q}{% \Delta P})
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Information Provided:
- Initial price ((P_1)) = 5 TL
- Initial quantity ((Q_1)) = 5 kg
- New quantity ((Q_2)) = 2 kg
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Calculate (\Delta Q):
\Delta Q = Q_2 - Q_1 = 2 - 5 = -3 \text{ kg} -
Percentage change in quantity ((% \Delta Q)):
\% \Delta Q = \left( \frac{\Delta Q}{Q_1} \right) \times 100 = \left( \frac{-3}{5} \right) \times 100 = -60\% -
Calculate (% \Delta P) using (E_d):
E_d = \frac{\% \Delta Q}{\% \Delta P} \Rightarrow -2 = \frac{-60}{\% \Delta P}\% \Delta P = \frac{-60}{-2} = 30\% -
Calculate new price ((P_2)):
- Since (% \Delta P = 30%), this indicates the price increases by 30%.
\Delta P = 30\% \text{ of } 5 \text{ TL} = 1.5 \text{ TL}P_2 = 5 + 1.5 = 6.5 \text{ TL}
Final Answer for Question 12:
The price of chicken should rise to 6.5 TL per kg for the family to demand 2 kg per month.
13. Demand Elasticity given M=20-3F
Question 13:
(M = 20 - 3F) talep fonksiyonunda (F = 4) iken talep esnekliği nedir?
Answer:
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Demand Function: (M = 20 - 3F)
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Find (Q_d) (Quantity Demanded) when (F = 4):
M = 20 - 3 \times 4 = 20 - 12 = 8 -
Calculate Elasticity ((E_d)):
The elasticity of a linear demand curve is given by:
E_d = \frac{dM/dF}{M/F}-
Calculate (dM/dF) (derivative of M with respect to F):
Since (M = 20 - 3F), (dM/dF = -3). -
Plug Values into Elasticity Formula:
For (F = 4), (M = 8):
E_d = \frac{-3}{8/4} = \frac{-3}{2} = -1.5 -
Final Answer for Question 13:
The elasticity at (F = 4) is (-1.5).
14. Arc Elasticity
Question 14:
F1=10 iken M1=25 ve F2=15 iken M2=40 ise:
a) Birinci noktadan ikinci noktaya geçişte arzın fiyat esnekliğini bulunuz?
b) İkinci noktadan birinci noktaya geçişte arzın fiyat esnekliğini bulunuz?
c) Yay (ark) esnekliğini bulunuz?
Answers:
a) Elasticity from first to second point
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Formula for Elasticity between two points ((E)):
E = \frac{\frac{\Delta Q}{\Delta P}}{\frac{(Q_1 + Q_2)}{2} \div \frac{(P_1 + P_2)}{2}} -
Values:
- (Q_1 = 25), (P_1 = 10)
- (Q_2 = 40), (P_2 = 15)
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Calculate (\Delta Q) and (\Delta P)
\Delta Q = Q_2 - Q_1 = 40 - 25 = 15\Delta P = P_2 - P_1 = 15 - 10 = 5 -
Plug into Elasticity Formula:
E = \frac{\left(\frac{15}{5}\right)}{\left(\frac{(25 + 40)}{70} \div \frac{(10 + 15)}{25}\right)}Simplifying expressions:
E = \frac{3}{\left(0.929 \div 1.0\right)} \approx 3.23
b) Elasticity from second to first point
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Use the absolute change values to calculate elasticity in the reverse direction.
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Since the formula structure is the same but reversed, the results will remain consistent numerically but depend on the average points.
c) Arc Elasticity:
- Use the calculated elasticity as arc elasticity due to identical averages in calculation for both scenarios.
Final Answer for Question 14:
a) (\approx 3.23), indicating the supplied elasticity moving from first to secondary point.
b) (\approx 3.23), similar results due to symmetrical calculation around midpoint.
c) Arc elasticity being approximately equal to calculated elasticities.
15. Income Elasticity of Demand
Question 15:
Tüketicinin geliri 10.000 TL’den 25.000 TL’ye yükseldiğinde talep ettiği aylık X malı miktarı 100 br’den 80 br’e düşüyorsa, X malının talebinin gelir esnekliğini hesaplayınız.
Answer:
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Income Elasticity of Demand ((E_i)):
Measures the responsiveness of quantity demanded due to changes in consumer income.
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Given:
- Initial income ((I_1)) = 10,000 TL
- New income ((I_2)) = 25,000 TL
- Initial quantity ((Q_1)) = 100
- New quantity ((Q_2)) = 80
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Calculate (\Delta I) and (\Delta Q):
\Delta I = I_2 - I_1 = 25,000 - 10,000 = 15,000 \text{ TL}\Delta Q = Q_2 - Q_1 = 80 - 100 = -20 -
Percentage changes:
\% \Delta Q = \frac{-20}{100} \times 100 = -20\%\% \Delta I = \frac{15,000}{10,000} \times 100 = 150\% -
Plugging into the Income Elasticity Formula:
E_i = \frac{\% \Delta Q}{\% \Delta I} = \frac{-20\%}{150\%} = -\frac{2}{15} \approx -0.13
Final Answer for Question 15:
The income elasticity of demand for X is approximately (-0.13), indicating it might be an inferior good as demand decreases with increased income.
16. Cross-Price Elasticity
Question 16:
A malının fiyatı 15 br’den 20 br’ye yükseldiğinde, B malının talebi 40 br’den 50 br’e artıyorsa, A ve B malları ne tür mallardır? Talebin çapraz esnekliğini hesaplayınız.
Answer:
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Cross-Price Elasticity of Demand ((E_{xy})):
Measures how the quantity demanded of one good changes as the price of another good changes.
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Given:
- Price of A increases: (15 \to 20) (initial (P_a = 15), new (P_a = 20))
- Demand of B increases: (40 \to 50) (initial (Q_b = 40), new (Q_b = 50))
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Calculate (\Delta P_a) and (\Delta Q_b):
\Delta P_a = 20 - 15 = 5\Delta Q_b = 50 - 40 = 10 -
Percentage changes:
\% \Delta Q_b = \frac{10}{40} \times 100 = 25\%\% \Delta P_a = \frac{5}{15} \times 100 = 33.33\% -
Cross-Price Elasticity Formula:
E_{xy} = \frac{\% \Delta Q_b}{\% \Delta P_a} = \frac{25\%}{33.33\%} \approx 0.75 -
Interpretation:
Positive cross-price elasticity implies A and B are substitutes.
Final Answer for Question 16:
A and B are substitute goods, and the cross-price elasticity is approximately (0.75).