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Given the following demand function for pork, [tex]Q = 1000 - 0.5P[/tex]:

a) By how much would the price have to fall for consumers to be willing to buy 1 kg of pork per day?

b) If the price increases by $0.7, by how much will quantity demanded change?

Sagot :

GinnyAnswer
Let's break this down step by step:

### Part (a)
We are given the demand function for pork:
[tex]\[ Q = 1000 - 0.5P \][/tex]

We need to find the price [tex]\( P \)[/tex] when the quantity demanded [tex]\( Q \)[/tex] is 1 kg. Essentially, we need to solve for [tex]\( P \)[/tex] in the equation with [tex]\( Q = 1 \)[/tex].

1. Substitute [tex]\( Q = 1 \)[/tex] into the demand function:
[tex]\[ 1 = 1000 - 0.5P \][/tex]

2. Rearrange the equation to solve for [tex]\( P \)[/tex]:
[tex]\[ 0.5P = 1000 - 1 \][/tex]
[tex]\[ 0.5P = 999 \][/tex]

3. Divide both sides by 0.5 to isolate [tex]\( P \)[/tex]:
[tex]\[ P = \frac{999}{0.5} \][/tex]
[tex]\[ P = 1998 \][/tex]

So, the price will have to be [tex]\( 1998 \)[/tex] for consumers to be willing to buy 1 kg of pork per day.

### Part (b)
Let's determine how the quantity demanded changes when the price increases by [tex]\( \$0.7 \)[/tex].

We know the demand function:
[tex]\[ Q = 1000 - 0.5P \][/tex]

1. Determine the change in quantity demanded ([tex]\( \Delta Q \)[/tex]) when the price increases by [tex]\( \$0.7 \)[/tex]:
[tex]\[ \Delta Q = -0.5 \times \Delta P \][/tex]

2. Substitute [tex]\( \Delta P = 0.7 \)[/tex]:
[tex]\[ \Delta Q = -0.5 \times 0.7 \][/tex]
[tex]\[ \Delta Q = -0.35 \][/tex]

Thus, if the price increases by [tex]\( \$0.7 \)[/tex], the quantity demanded will decrease by [tex]\( 0.35 \)[/tex] kg.

### Summary:
- To buy 1 kg of pork per day, the price should fall to [tex]\( \$1998 \)[/tex].
- If the price increases by [tex]\( \$0.7 \)[/tex], the quantity demanded will decrease by [tex]\( 0.35 \)[/tex] kg.
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