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Sagot :
Alright, let's delve into the problem step-by-step.
We are given the demand and supply functions for the market for apples:
- Demand: [tex]\( Q_d = 32 - 2p \)[/tex]
- Supply: [tex]\( Q_s = 4p - 10 \)[/tex]
where [tex]\( Q_d \)[/tex] is the quantity demanded, [tex]\( Q_s \)[/tex] is the quantity supplied, and [tex]\( p \)[/tex] is the price in GHS.
Part a): Calculate the quantity demanded and quantity supplied at different prices.
i) For GHS 3.00:
1. Quantity Demanded:
- Demand function: [tex]\( Q_d = 32 - 2p \)[/tex]
- Substitute [tex]\( p = 3.00 \)[/tex]:
[tex]\[ Q_d = 32 - 2 \times 3.00 = 32 - 6 = 26.0 \][/tex]
2. Quantity Supplied:
- Supply function: [tex]\( Q_s = 4p - 10 \)[/tex]
- Substitute [tex]\( p = 3.00 \)[/tex]:
[tex]\[ Q_s = 4 \times 3.00 - 10 = 12 - 10 = 2.0 \][/tex]
So, for a price of GHS 3.00, the quantity demanded is 26.0, and the quantity supplied is 2.0.
ii) For GHS 10.00:
1. Quantity Demanded:
- Demand function: [tex]\( Q_d = 32 - 2p \)[/tex]
- Substitute [tex]\( p = 10.00 \)[/tex]:
[tex]\[ Q_d = 32 - 2 \times 10.00 = 32 - 20 = 12.0 \][/tex]
2. Quantity Supplied:
- Supply function: [tex]\( Q_s = 4p - 10 \)[/tex]
- Substitute [tex]\( p = 10.00 \)[/tex]:
[tex]\[ Q_s = 4 \times 10.00 - 10 = 40 - 10 = 30.0 \][/tex]
So, for a price of GHS 10.00, the quantity demanded is 12.0, and the quantity supplied is 30.0.
iii) For GHS 14.00:
1. Quantity Demanded:
- Demand function: [tex]\( Q_d = 32 - 2p \)[/tex]
- Substitute [tex]\( p = 14.00 \)[/tex]:
[tex]\[ Q_d = 32 - 2 \times 14.00 = 32 - 28 = 4.0 \][/tex]
2. Quantity Supplied:
- Supply function: [tex]\( Q_s = 4p - 10 \)[/tex]
- Substitute [tex]\( p = 14.00 \)[/tex]:
[tex]\[ Q_s = 4 \times 14.00 - 10 = 56 - 10 = 46.0 \][/tex]
So, for a price of GHS 14.00, the quantity demanded is 4.0, and the quantity supplied is 46.0.
Part b): Now, we need to address the calculation of the elasticity of demand for apples.
However, this part of the question is not fully outlined in the initial problem statement, and additional information such as the midpoint formula or the definition you'd prefer to use for elasticity is required. Elasticity of demand generally measures the responsiveness of the quantity demanded to a change in price. The formula for the price elasticity of demand is typically given by:
[tex]\[ E_d = \frac{\Delta Q_d / Q_{d\_avg}}{\Delta p / p_{avg}} \][/tex]
where [tex]\(\Delta Q_d\)[/tex] is the change in quantity demanded, [tex]\(Q_{d\_avg}\)[/tex] is the average quantity demanded, [tex]\(\Delta p\)[/tex] is the change in price, and [tex]\(p_{avg}\)[/tex] is the average price.
Since this was not provided, ensure to let me know if more elaboration or specific computations are needed for this part.
We are given the demand and supply functions for the market for apples:
- Demand: [tex]\( Q_d = 32 - 2p \)[/tex]
- Supply: [tex]\( Q_s = 4p - 10 \)[/tex]
where [tex]\( Q_d \)[/tex] is the quantity demanded, [tex]\( Q_s \)[/tex] is the quantity supplied, and [tex]\( p \)[/tex] is the price in GHS.
Part a): Calculate the quantity demanded and quantity supplied at different prices.
i) For GHS 3.00:
1. Quantity Demanded:
- Demand function: [tex]\( Q_d = 32 - 2p \)[/tex]
- Substitute [tex]\( p = 3.00 \)[/tex]:
[tex]\[ Q_d = 32 - 2 \times 3.00 = 32 - 6 = 26.0 \][/tex]
2. Quantity Supplied:
- Supply function: [tex]\( Q_s = 4p - 10 \)[/tex]
- Substitute [tex]\( p = 3.00 \)[/tex]:
[tex]\[ Q_s = 4 \times 3.00 - 10 = 12 - 10 = 2.0 \][/tex]
So, for a price of GHS 3.00, the quantity demanded is 26.0, and the quantity supplied is 2.0.
ii) For GHS 10.00:
1. Quantity Demanded:
- Demand function: [tex]\( Q_d = 32 - 2p \)[/tex]
- Substitute [tex]\( p = 10.00 \)[/tex]:
[tex]\[ Q_d = 32 - 2 \times 10.00 = 32 - 20 = 12.0 \][/tex]
2. Quantity Supplied:
- Supply function: [tex]\( Q_s = 4p - 10 \)[/tex]
- Substitute [tex]\( p = 10.00 \)[/tex]:
[tex]\[ Q_s = 4 \times 10.00 - 10 = 40 - 10 = 30.0 \][/tex]
So, for a price of GHS 10.00, the quantity demanded is 12.0, and the quantity supplied is 30.0.
iii) For GHS 14.00:
1. Quantity Demanded:
- Demand function: [tex]\( Q_d = 32 - 2p \)[/tex]
- Substitute [tex]\( p = 14.00 \)[/tex]:
[tex]\[ Q_d = 32 - 2 \times 14.00 = 32 - 28 = 4.0 \][/tex]
2. Quantity Supplied:
- Supply function: [tex]\( Q_s = 4p - 10 \)[/tex]
- Substitute [tex]\( p = 14.00 \)[/tex]:
[tex]\[ Q_s = 4 \times 14.00 - 10 = 56 - 10 = 46.0 \][/tex]
So, for a price of GHS 14.00, the quantity demanded is 4.0, and the quantity supplied is 46.0.
Part b): Now, we need to address the calculation of the elasticity of demand for apples.
However, this part of the question is not fully outlined in the initial problem statement, and additional information such as the midpoint formula or the definition you'd prefer to use for elasticity is required. Elasticity of demand generally measures the responsiveness of the quantity demanded to a change in price. The formula for the price elasticity of demand is typically given by:
[tex]\[ E_d = \frac{\Delta Q_d / Q_{d\_avg}}{\Delta p / p_{avg}} \][/tex]
where [tex]\(\Delta Q_d\)[/tex] is the change in quantity demanded, [tex]\(Q_{d\_avg}\)[/tex] is the average quantity demanded, [tex]\(\Delta p\)[/tex] is the change in price, and [tex]\(p_{avg}\)[/tex] is the average price.
Since this was not provided, ensure to let me know if more elaboration or specific computations are needed for this part.
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