Math / Algebra

Question2. The demand function for a certain good is given by $Q_{d}=1500-5 P$ , the supply function is: $Q_{s}=200+5 P$ . The government decided to set the price of this good at $P=140 \mathrm{zt}$ and committed itself to intervene at the market to correct for the possible effects of a market disequilibrium. What will be the costs of this intervention - if any? (3)

Studdy Solution

STEP 1

What is this asking? If the government sets a fixed price, will there be extra goods or not enough goods, and how much will it cost the government to fix the problem? Watch out! Don't mix up supply and demand!
A high price means suppliers want to make more, and buyers want to buy less.

STEP 2

1. Calculate Demand
2. Calculate Supply
3. Calculate Surplus/Shortage
4. Calculate Cost of Intervention

STEP 3

Let's plug in the given price, $P = 140$ , into the demand function: $Q_d = 1500 - 5 \cdot P$ $Q_d = 1500 - 5 \cdot 140$

STEP 4

Calculate the demand at this price: $Q_d = 1500 - 700$ $Q_d = 800$ So, at a price of $\$140$ , people want to buy 800 units of the good.

STEP 5

Now, let's plug in the same price, $P = 140$ , into the supply function: $Q_s = 200 + 5 \cdot P$ $Q_s = 200 + 5 \cdot 140$

STEP 6

Calculate the supply at this price: $Q_s = 200 + 700$ $Q_s = 900$ So, at a price of $\$140$ , suppliers want to produce 900 units of the good.

STEP 7

We see that $Q_s$ is greater than $Q_d$ .
This means there's more supply than demand, which creates a surplus.

STEP 8

Let's calculate the surplus: $Surplus = Q_s - Q_d$ $Surplus = 900 - 800$ $Surplus = 100$ There's a surplus of 100 units.

STEP 9

The government has to buy the surplus to maintain the price.
The cost of the intervention is the surplus multiplied by the price per unit.

STEP 10

Calculate the cost: $Cost = Surplus \cdot P$ $Cost = 100 \cdot 140$ $Cost = 14000$ The cost of the intervention is $\$14000$ .

STEP 11

The cost of the government intervention will be $\$14,000$ .

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Studdy Solution

STEP 1

What is this asking? If the government sets a fixed price, will there be extra goods or not enough goods, and how much will it cost the government to fix the problem? Watch out! Don't mix up supply and demand!
A high price means suppliers want to make more, and buyers want to buy less.

STEP 2

1. Calculate Demand
2. Calculate Supply
3. Calculate Surplus/Shortage
4. Calculate Cost of Intervention

STEP 3

Let's plug in the given price, $P = 140$ , into the demand function: $Q_d = 1500 - 5 \cdot P$ $Q_d = 1500 - 5 \cdot 140$

STEP 4

Calculate the demand at this price: $Q_d = 1500 - 700$ $Q_d = 800$ So, at a price of $\$140$ , people want to buy 800 units of the good.

STEP 5

Now, let's plug in the same price, $P = 140$ , into the supply function: $Q_s = 200 + 5 \cdot P$ $Q_s = 200 + 5 \cdot 140$

STEP 6

Calculate the supply at this price: $Q_s = 200 + 700$ $Q_s = 900$ So, at a price of $\$140$ , suppliers want to produce 900 units of the good.

STEP 7

We see that $Q_s$ is greater than $Q_d$ .
This means there's more supply than demand, which creates a surplus.

STEP 8

Let's calculate the surplus: $Surplus = Q_s - Q_d$ $Surplus = 900 - 800$ $Surplus = 100$ There's a surplus of 100 units.

STEP 9

The government has to buy the surplus to maintain the price.
The cost of the intervention is the surplus multiplied by the price per unit.

STEP 10

Calculate the cost: $Cost = Surplus \cdot P$ $Cost = 100 \cdot 140$ $Cost = 14000$ The cost of the intervention is $\$14000$ .

STEP 11

The cost of the government intervention will be $\$14,000$ .

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Studdy Solution

STEP 1

What is this asking? If the government sets a fixed price, will there be extra goods or not enough goods, and how much will it cost the government to fix the problem? Watch out! Don't mix up supply and demand!A high price means suppliers want to make more, and buyers want to buy less.

STEP 2

1. Calculate Demand2. Calculate Supply3. Calculate Surplus/Shortage4. Calculate Cost of Intervention

STEP 3

Let's **plug in** the given price, P=140P = 140P=140, into the **demand function**: Qd=1500−5⋅PQ_d = 1500 - 5 \cdot PQd​=1500−5⋅P Qd=1500−5⋅140Q_d = 1500 - 5 \cdot 140Qd​=1500−5⋅140

STEP 4

**Calculate** the **demand** at this price: Qd=1500−700Q_d = 1500 - 700Qd​=1500−700 Qd=800Q_d = 800Qd​=800So, at a price of $140\$140$140, people want to buy **800** units of the good.

STEP 5

Now, let's **plug in** the same price, P=140P = 140P=140, into the **supply function**: Qs=200+5⋅PQ_s = 200 + 5 \cdot PQs​=200+5⋅P Qs=200+5⋅140Q_s = 200 + 5 \cdot 140Qs​=200+5⋅140

STEP 6

**Calculate** the **supply** at this price: Qs=200+700Q_s = 200 + 700Qs​=200+700 Qs=900Q_s = 900Qs​=900So, at a price of $140\$140$140, suppliers want to produce **900** units of the good.

STEP 7

We see that QsQ_sQs​ is **greater** than QdQ_dQd​.This means there's more supply than demand, which creates a **surplus**.

STEP 8

Let's **calculate** the **surplus**: Surplus=Qs−QdSurplus = Q_s - Q_dSurplus=Qs​−Qd​ Surplus=900−800Surplus = 900 - 800Surplus=900−800Surplus=100Surplus = 100Surplus=100There's a surplus of **100** units.

STEP 9

The government has to buy the **surplus** to maintain the price.The cost of the intervention is the **surplus** multiplied by the **price per unit**.

STEP 10

**Calculate** the **cost**: Cost=Surplus⋅PCost = Surplus \cdot PCost=Surplus⋅P Cost=100⋅140Cost = 100 \cdot 140Cost=100⋅140Cost=14000Cost = 14000Cost=14000The cost of the intervention is $14000\$14000$14000.

STEP 11

The cost of the government intervention will be $14,000\$14,000$14,000.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? If the government sets a fixed price, will there be extra goods or not enough goods, and how much will it cost the government to fix the problem? Watch out! Don't mix up supply and demand!
A high price means suppliers want to make more, and buyers want to buy less.

1. Calculate Demand
2. Calculate Supply
3. Calculate Surplus/Shortage
4. Calculate Cost of Intervention

Let's plug in the given price, $P = 140$ , into the demand function: $Q_d = 1500 - 5 \cdot P$ $Q_d = 1500 - 5 \cdot 140$

Calculate the demand at this price: $Q_d = 1500 - 700$ $Q_d = 800$ So, at a price of $\$140$ , people want to buy 800 units of the good.

Now, let's plug in the same price, $P = 140$ , into the supply function: $Q_s = 200 + 5 \cdot P$ $Q_s = 200 + 5 \cdot 140$

Calculate the supply at this price: $Q_s = 200 + 700$ $Q_s = 900$ So, at a price of $\$140$ , suppliers want to produce 900 units of the good.

We see that $Q_s$ is greater than $Q_d$ .
This means there's more supply than demand, which creates a surplus.

Let's calculate the surplus: $Surplus = Q_s - Q_d$ $Surplus = 900 - 800$ $Surplus = 100$ There's a surplus of 100 units.

The government has to buy the surplus to maintain the price.
The cost of the intervention is the surplus multiplied by the price per unit.

Calculate the cost: $Cost = Surplus \cdot P$ $Cost = 100 \cdot 140$ $Cost = 14000$ The cost of the intervention is $\$14000$ .

The cost of the government intervention will be $\$14,000$ .