All formulas and calculations needed in Paper 2 Paper 3 - IB Economics

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All formulas and calculations needed in Paper 2 Paper 3 - IB Economics

Mr Lee - Business Econ 16.04.2026 2 157 просмотров 82 лайков

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#IBEconomics #EconomicsCalculations #IBPaper3 In this video, we cover every calculation required for Paper 2 and Paper 3. This guide is designed to show you exactly how to approach these quantitative questions accurately under exam conditions. This video will illustrate and analyze the precise mathematical requirements to achieve maximum marks. First, we will examine microeconomic calculations, specifically how to calculate elasticities, the impact of government interventions like taxes and subsidies, and firm profitability. Next, we look at macroeconomic formulas, focusing on how to accurately calculate GDP, inflation, unemployment, and the Keynesian multiplier. We will also analyze global economy quantitative skills, demonstrating how to determine comparative advantage, exchange rate fluctuations, and the numerical effects of trade protection on stakeholders. Crucially, this comprehensive review is fully aligned with the post-2022 syllabus, ensuring you are studying exactly what is needed without wasting time on outdated requirements like linear demand functions. Timestamps: 00:00 - Intro 00:35 - Consumer surplus 02:56 - Producer surplus 04:32 - PED 05:34 - PES 06:22 - YED 07:20 - Indirect tax revenue 07:47 - Price ceilings 09:23 - Price floors 10:05 - Indirect tax 10:45 - Subsidies 12:01 - Effect on spending 13:03 - Effect on welfare 13:55 - Average revenue/cost 14:32 - Marginal revenue 15:11 - Marginal cost 15:47 - Profit 16:31 - Profit (Diagram) 17:50 - Nominal GDP 18:23 - Nominal GNI 19:16 - Real GDP & GNI 19:57 - Per capita 20:58 - Unemployment rate 21:46 - CPI basket 22:44 - Weighted price index 23:52 - Indirect tax 24:24 - Regressive tax 25:05 - Proportional tax 25:42 - Keynesian multiplier 26:10 - Effect on GDP 26:37 - Free trade 28:06 - Exports 28:58 - Imports 29:29 - Economic growth rate 29:47 - Comparative adv 30:39 - Tariff 31:50 - Quotas 32:58 - Expenditure 33:39 - Currency pricing 34:27 - Currency value 35:18 - Current account

Оглавление (41 сегментов)

Intro

In this video, I'm going to be guiding you through every calculation for the IB economics for paper two and paper three. And for your convenience, here are the timestamps for this video. There are only three ways that the IB presents data to students. One way is just writing some text like this. The other will be in a table. And the last one will be a diagram. And all these will have some numerical data in there for you to calculate. So, let's start the calculations.

Consumer surplus

Calculate the change of the consumer surplus after the imposition of the price ceiling of $5. The old consumer surplus is this triangle here. So, we take the maximum price that people are willing to pay, which is $14 according to this diagram. And then we subtract the old equilibrium price, which is $6. This gives us the value of this line here. We know at the old equilibrium, the quantity demanded was 8,000 kg. So, if we do the calculation, this is 14 - 6, which gives us 8 multiplied by 8. And then divide that answer by two. Because it is a triangle, this gives us the answer of 32. We are now going to calculate the new consumer surplus. We're going to start with the triangle at the top. Since there is a price ceiling, only 6,000 kg are made. And for the people that who are willing and able to pay a range from 14 to $8 for these 6,000 kg were able to buy their products. And anyone that was not willing to pay more than $8 simply did not get a product to buy. We know that the new quantity with the price ceiling is 6,000 kg, which is illustrated here at the price of $8. And the maximum amount people are willing to pay is again $14. And to work this line out, this is 14 - 8, which is represented here. So, 14 - 8 = 6. We multiply this by 6, which is the quantity. Then we divide it by two because it is a triangle. And that gives us the answer of 18. And now we need to finish off calculating the consumer surplus by adding the area of the rectangle in below. In this case, 8 - 5, which is 3, multiplied by 6, which is the quantity. Which gives the answer 18. And now we add the new triangle and the new rectangle together, which is 18 + 18. This gives us 36. And as they are asking us the change in consumer surplus, this is the new consumer surplus minus the old consumer surplus, which is 36 - 32, which is four. And as the quantity is in the thousands, the answer is $4,000.

Producer surplus

Using figure one, calculate the impact of this tax on the producer surplus for the island nation's fishermen. Now, in this diagram, we can see that at the equilibrium before the tax is $16. And the price that they were willing to receive at zero quantity is $2, which is illustrated here. And at the price of $16, suppliers were willing to supply 28,000 kg per year. So, in our case, how to calculate this triangle is 16 - 2, which gives us 14 multiplied by 28, which gives us 392 divided by two because this is a triangle. Which gives us the number of 196. The new price received after the tax by producers is $14. And the price that they are willing to receive is the same at $2 at a quantity of zero, which gives us this line here. And according to this diagram, at $14, producers are willing to only supply 24,000 kg. And then if we calculate the area of the new triangle, which is 14 - 2, which gives us 12 multiplied by 24, which gives us 288 divided by two because it is a triangle. This gives us the answer of 144. And the change in the surplus is 196 - 144, which is 52. And since our quantity is in the thousands, the answer is $52,000.

PED

Using the information in figure one, calculate the price elasticity of demand for capsicums when the price increases from $18 per kilo to $24 per kilo. The formula to PED is percentage change in quantity demanded divided by the percentage change in price. And how to calculate percentage change is new minus old divided by old times 100. So, in this case, before the tax, the quantity demanded was 55,000 kilos and after the tax, 40,000. So, we take 40 - 55 divided by 55 * 100. This gives us 27. 27%, which is the change in quantity demanded. And we do the same for the percentage change in price. According to the diagram, the new price is $24 minus the old price of $18 divided by $18 * 100, which gives us

PES

Using the information in figure two, calculate the price elasticity of supply for tea. We can see that the new quantity is 4,800 and the old quantity is 3,700. So, new minus old divided by old times 100 is 29. 73%. And for the percentage change in price, the new price is 340 KES minus the old price, which is 324 KES divided by 324 * 100. And that gives us 4. 94%. So, if we divide the percentage change in quantity supplied over the percentage change in price, which is 29. 74% divided by 4. 94%, this gives us the answer of 6. 02.

YED

A middle-income household in the Philippines earned 4,000 pesos weekly in 2021. Its weekly income increased to 4,200 pesos in 2022. Its weekly demand for rice decreased from 4 kg to 3. 9 kg between '21 and '22. Calculate the income elasticity of demand for rice for this household. Using the same formula, new minus old divided by old, this is 3. 9 kg minus 4 kg divided by 4 multiplied by 100, and this gives us the answer of minus 2. 5. And the percentage change in income is 4,200 pesos minus 4,000 pesos divided by 4,000 multiplied by 100, and that gives us the answer of five. So, YED = -2. 5 divided by 5. And this gives us the answer of minus 0. 5.

Indirect tax revenue

A specific tax of $2 is imposed on the product. Following the tax, the equilibrium quantity sold is 450,000 units. Calculate the total tax revenue collected by the government. As we know, there is a $2 tax per unit, and the quantity is 450,000. So, this is 2 multiplied by 450,000, and the answer is $900,000.

Price ceilings

Calculate the change in consumer expenditure on butter per month resulting from the imposition of the price ceiling. As we can see, initially, the price per unit is $14, and the quantity per period is 800,000 kg. And in order to calculate consumer expenditure, we need to multiply the price by the quantity. And 14 * 800 is 11,200. And we know that this red line here represents excess demand. And with the price ceiling, the price on the diagram is $10. And in the case of the quantity, here we need to zoom in. When we zoom in like this, you can tell that every small square here represents two units. So, if we have a look at the equilibrium here and then we trace it down to the quantity, which is here. The quantity here is 784. Now, zooming back out, you can see that the expenditure with ceiling is $10 multiplied by 784, and this gives us 7,840. And since that the question is asking us for the change, what we need to do is to subtract them from each other, which is new minus old, and that gives us minus $3,360. I apologize there. As the quantity per period is in the thousands of kilograms, the answer is minus $3. 36 million.

Price floors

To support farmers, the government sets a price floor for wheat at $250 per ton. At this price, consumers demand 4,000 tons, while producers supply 6,000 tons. Calculate the total cost to the government if it purchases the entire surplus to maintain the price floor. As you can see, the surplus is 6,000 - 4,000 as there are 6,000 tons in supply and 4,000 tons demanded, which gives us an excess of 2,000. And the price floor is $250. And therefore, the total cost to the government is 2,000 tons multiplied by 250 $250 and the answer is $500,000.

Indirect tax

Using figure two, calculate the revenue in rupees per day collected from the indirect taxes on petrol in New Delhi. For this question, you needed to extract the appropriate data from two sources of data. The first bit of data we need is the tax per unit, which we get here. Which is 50 rupees per unit. And in order to find the quantity, we need to look at the equilibrium on the diagram. And we can see that the quantity at the equilibrium is 500 million. So, we multiply the quantity and the tax together and that gives us 25 billion rupees.

Subsidies

rupees. Figure three illustrates the market for cotton in the country of San Marcos, a small closed economy. Cotton is used as an input in the San Marcos textile industry. Quantity is in the thousands of kilograms. Calculate the cost to the government of San Marcos for providing the subsidy to domestic cotton producers. Let's zoom into the diagram and see how much the subsidy is. As we all know that the distance between the supply curves is the value of the subsidy. The price before the subsidy is $10. And if we draw a vertical line down until we hit the S plus sub, this gives us a price of $2. So, now we have calculated the value of the subsidy, which is $8. So, now we can easily calculate the government expenditure. As the subsidy is $8 and the new quantity is 75. Let me show you. You can see that every small square here is worth five units. With the subsidy, this is 75 units. And as the government is spending $8 per unit and they are selling 75 units, the answer is $600,000 as the quantity is measured in thousands of kilograms.

Effect on spending

The government of Islandia wants to reduce the price of rice by 40% in order to enable low-income households to buy enough rice to meet their needs. The government decides to achieve this by imposing a maximum price. Calculate the change in consumer expenditure on rice resulting from the imposition of the maximum price. Firstly, we need to calculate the old expenditure, which is price per kilogram is $5 and the quantity of rice was 200. And if we multiply these together, this gives us $1,000. Remember that there is a limited supply available due to the price ceiling and this is 100 as suppliers are only willing to supply this amount to the market and the price with the maximum price is $3. So, the new expenditure is $3 multiplied by 100 and this gives us $300 and the difference between the two is $1,000 minus $300, which is minus $700,000 as the quantity of rice is measured in the thousands.

Effect on welfare

The following diagram illustrates the domestic market for rice in country Alpha. The government in Alpha imposes a rice ceiling of $5 per kilogram. Calculate the welfare loss after the imposition of the price ceiling. Now, the welfare loss is this triangle here and the value of this line is 8 minus five, which is $3. And we know that the quantity at the equilibrium was eight and with the price ceiling, it is six, so the difference is two. So, in order to calculate the welfare loss, we have three multiplied by two divided by two as it is a triangle and the result is $3,000 as the quantity per year is in thousands of kilograms.

Average revenue/cost

Calculate the average cost and the average revenue. The formula for average revenue is total revenue divided by the output. So, in this case, the total revenue is 10, which is the output multiplied by 50, which is the price. That gives us 500. So, the average revenue is 500 divided by the output, which is 10. The average revenue is $50. And we do the same calculation for the total cost and the total cost is 400 and the average cost is 400 over 10. So, $40 per unit.

Marginal revenue

average cost is $40 per unit. Using table one, calculate the marginal revenue if the number of members increase from 300 to 400 per month. The formula to calculating marginal revenue is the change in total revenue divided by the change in quantity. So, we get the old total revenue, which is 400 multiplied by 90, which is 36,000 minus the new total revenue, which is 300 multiplied by 100, which is 30,000 and the quantity is 400 minus 300, which gives us 100. So, 6,000 divided by 100 is $60.

Marginal cost

A small firm produces handmade candles. The table below shows its total cost at different output levels per week. The formula to calculating marginal cost is the change in total cost over the change in quantity. So, in this case, the total cost for 22 units is $1,120 minus $1,000, which is for 20 units and the answer is 120. And then we do the same for the quantity, which is 22 units minus 20, which gives us two. So, that's 120 divided by two and that gives us the answer of $60.

Profit

Using table one, calculate the increase in profit if the number of members increase from 400 to 500 per month. So, firstly, we need to work out the old total revenue, which is 400 multiplied by 90. Then we need to subtract the monthly total cost, which is 21,600 and that gives us 14,400. And the new total revenue is 500 multiplied by 80 and we subtract the monthly total cost of 24,700 and that gives us the answer of 15,300. So, the difference between the two of them is 15,300 minus 14,400 and the answer is $900.

Profit (Diagram)

Calculate firm A's short-run abnormal profit or loss at the level of output. So, here, let's zoom in. In this diagram, it appears that they want to trick us because AR also equals MR. As we know, the profit-maximizing level is MC equals MR. And the quantity in this diagram when MC equals MR is 140. We can see that the average revenue here is $18. And the average cost at this quantity of 140 per month is $14. So, now we can go back to do our calculations. So, [snorts] at the profit-maximizing level of MC equals MR, average revenue is 18 multiplied by 140, which gives us 2,520. The average cost is 14 multiplied by 140, which gives us 1,960. So, average revenue minus average cost is 2,520 minus 1,960, which is $560,000 as quantity per month is in the thousands.

Nominal GDP

Using the information from table three, calculate the nominal GDP growth rate from Mexico for 2016. If the real growth rate is minus inflation, then the nominal growth rate is plus inflation. So, the key bits of data that we need from this table is the real growth rate in 2016, which is 2. 1 and the inflation rate of 2. 7, which is here. So, 2. 1 plus 2. 7, the answer is 4. 8%.

Nominal GNI

Calculate nominal GNI in 2015. Enter your result in table two. Just a reminder, the formula to GNI is nominal GDP minus net income. In this case, the income earned from abroad is 9. 49 and the income sent abroad is 75. 9. So, in order to get the net income is income earned minus income sent, which is 9. 49 minus 75. 9. This gives us minus 66. 41. We can see that the nominal GDP is 358. 97. So, this number minus 66. 41 292. 56 billion — [clears throat] — as these numbers are measured in the billions. Calculate the real GDP using the GDP

Real GDP & GNI

deflator. And the calculation is very straightforward, which is the nominal GDP divided by the GDP deflator. In 2018, this is 100 divided by 100 * 100 = 100 billion, which is the base year. In 2019, this is 110 divided by 105 multiplied by 100. This gives us 104. 76 billion. And in 2020, this is 120 divided by 110 multiplied by 100, which is 109. 09 billion.

Per capita

billion. In 2020, country A has a real GDP of 109. 09 billion and a total population of 50 million people. Calculate the real GDP per capita. This one is relatively straightforward as the real GDP divided by the population is the calculation. So, this is 109. 09 billion divided by 50 million and the answer is 2,181. 8 real GDP per capita. A country's real GDP was 400 billion in 2019 and increased to 420 billion. Calculate the rate of economic growth for the year 2020. As per usual, we do the new minus old divided by old method. So, this is the change in real GDP of 420 minus 400. This gives us 20, which we divide by 400 * 100 and the answer is 5%.

Unemployment rate

Calculate the unemployment rate in Fairland using table one. We know that the working age population is 231 million people. And the data shows us that 62% of them are working. And 62% of 231 million people is 143 million. And now that 143 million people are either employed or unemployed, we subtract the employed people, which is 105 million, which gives us 38 million people. This means that 38 million people of 143 million people are unemployed. And as a percentage, we divide them together and that's 26. 57%.

CPI basket

A simplified consumer basket contains two items, food and clothing. Calculate the inflation rate between 2019 and 2020. So, we need to work out the value in 2019 for both food and clothing. And we do the same for 2020. So, in 2019, food was $2 at 10 units plus the clothing, which was five units at $10, which gives us a total of $70 in 2019. And in 2020, we had 10 units of food at 2 and 1/2 dollars and five units of clothes at 11 dollars. And the value in 2020 was $80. As per usual, we do the new minus old, which is 80 minus 70 divided by old, which is 70 * 100. The answer is 14. 29%. Apologies for the error in the brackets here.

Weighted price index

A price index is calculated by using weights for three categories, housing, food, and transport. Calculate the total weighted price index. Firstly, we need to find the weighted values for each category, which is housing, food, and transport. So, housing is 60 multiplied by 120. Food is 30 multiplied by 150. And transport is 10 multiplied by 110. And the total sum of these values is 7,200 + 4,500 + 1,100. And that gives us the answer of 12,800. The next thing we need to do is find out the total weight. And the total weight is housing plus food plus transport. So, in this case, 60 + 30 + 10. That gives us the answer of 100. So, we divide 12,800 by 100. And the total weighted price index is 128. This means that on average, prices for this basket of goods has risen by 28% since the base year.

Indirect tax

A consumer spends $600 on a smartphone in the country with a 20% value added tax included in the price. Calculate the amount of indirect tax paid from this expenditure. We know that the expenditure is $600. And the price excluding tax is $600 divided by 1. 2, which essentially we're taking 20% away, which gives us $500. So, the tax paid is 600 minus 500. And the answer is $100.

Regressive tax

A country uses a poll tax, which is a flat rate of $2,000 regardless of income. Calculate the average tax rate for a low income earner versus a high income earner. For the low income earner, they earn $20,000 and they pay $2,000 in tax. So, the average tax rate is $2,000 divided by 20,000 * 100, which gives us 10%. And the calculation for the high income earner is still $2,000 divided by their income, which is $100,000 * 100, which is 2%. So, the low income earner pays 10% and the high income earner pays 2%.

Proportional tax

A country uses a flat tax where everyone pays 10% of their income. Calculate the total tax paid and the average tax rate for an earner making $50,000. As their income is $50,000, their tax paid is $50,000 multiplied by 0. 1, which gives us the dollar amount of how much they pay in tax. So, the average tax rate is $5,000 divided by $50,000 * 100. So, the answer is 10% and $5,000 in tax.

Keynesian multiplier

The government identifies that the marginal propensity to consume in the economy is 0. 2. Calculate the value of the Keynesian multiplier. The formula for this is 1 over 1 minus MPC. So, if we put the units in, that is 1 divided by 0. 8 as we have subtracted 0. 2 from 1 = 1. 25. So, the Keynesian multiplier is 1. 25.

Effect on GDP

The government invests $100,000 into the economy. Determine the size of the total increase in real national output given a multiplier of 1. 25. The formula here is the Keynesian multiplier multiplied by the injection. So, in this case, 1. 25 multiplied by 100,000. And the answer is $125,000.

Free trade

Calculate the social surplus earned by stakeholders in the coffee market in country X under conditions of free trade. Okay, let's zoom in to get a better look. As we can see here, this is the maximum price that consumers are willing to pay at zero output, which is 4. 6. And the equilibrium price on this diagram is $3. So, the value of this side of the triangle is 4. 6 minus 3, which gives us 1. 6. And the quantity at this equilibrium is 20. So, the calculation here is 1. 6 multiplied by 20 divided by 2 as it is a triangle, which gives us the value of 16. And in the case for the producer surplus, the equilibrium price that they are willing to sell is $3 and the minimum price at zero quantity is 1. As this is an exporting country, the equilibrium is when the domestic supply intersects with the world price. And this gives us a quantity of 200. So, the calculation is 2 * 200 divided by 2, which gives us 200. And if we add the two together, 16 + 200, the community surplus is 216,000 as the quantity of coffee is measured in the thousands of kilograms.

Exports

Calculate the value of coffee exports per year from country X. First, we need to find out the quantity of coffee exported out of the country. And that is represented in the blue line here. We can see that at the world price of $3, the domestic demand is at 20,000 kilograms. And since that domestic producers are making 200,000 kilograms here, this means that the blue line here is all exported. And the value of this blue line is 200 minus 20, which gives us 180. And then we multiply that by $3 and this gives us the answer of 540,000 as the quantity of coffee is measured in the thousands of kilograms.

Imports

In the market for specialized machinery in Kenya, the domestic price is very high. The world price is $10,000. At this price, domestic demand is 500 units. But domestic firms can only supply 100 units. Calculate the quantity of imports and the total import expenditure. Let's calculate the quantity of imports first. Firstly, we know that the domestic demand is 500 units. But they only supply 100 domestically. Therefore, the imports will need to be

Economic growth rate

400 units, which is 500 minus 100. And as we know the quantity of imports is 400 units at the world price of $10,000, Kenya will need to be spending 400 multiplied by 10,000 on their imports, which is $4 million.

Comparative adv

Two countries, country A and country B, produce two goods, rice and computers. The table shows their maximum possible output using all resources. Calculate the opportunity cost to identify which country has the comparative advantage in rice. Since that the question is asking about rice, this means that we will need to sacrifice our computers. So, we're going to sacrifice our 50 computers, and we're going to divide it by 100, which is our rice. 50 / 100 is 0. 5. This means that every time country A produces one bag of rice, it costs them 0. 5 of a computer to make. We'll do the same calculation for country B, which is 40 / 40 = 1. Therefore, country A has the lower opportunity cost and the comparative advantage.

Tariff

Okay, so we have some data here. So, 1 TL equals 0. 134 US dollars. Calculate in TL the change in the monthly total revenues of Turkish wheat producers as a result of the elimination of the 20% tariff. Let's work out the total revenues first. With the tariff, the Turkish wheat producers are receiving $7. 20 and they are producing 36 million kilograms. And when the tariff is removed, the price drops to six and the quantity falls to 30 million kilograms. So, let's have a look at these numbers. The total revenue with the tariff was 259. 2 and without the tariff, 180. And the difference between the two is minus 79. 2 US dollars. Since 1 TL is 0. 134 US dollars, we'll take the answer minus 79. 2 divided by 0. 134 and that gives us the answer of minus 591. 04 million TL.

Quotas

The world price of bananas is $3. The government of country A decides to impose a quota on banana imports of 150,000 kilograms per month. Calculate the change in revenue earned by domestic producers of bananas in the country A as a result of the quota. Let's zoom into the diagram to get a clearer view. The initial revenue from domestic producers was $3 multiplied by the quantity of 50. As this was the market price and quantity before the quota. And because of this quota, the price of bananas increase. And as the price increases, there is an incentive for domestic producers to produce more. As the price is now $5 and the quantity 150. So, let's have a look at the numbers. The initial revenue was 3 multiplied by 50, which is 150. And the final revenue is 5 multiplied by 150 = 750. And the difference between the two is 750 - 150. That gives us the answer of $600,000.

Expenditure

Referring to the steel tariffs, before the tariffs, consumers bought 800 units at $400. And after the tariff, consumers bought 700 units at $500. Calculate the change in total consumer expenditure. Firstly, we calculate before the tariff, which is 800 units multiplied by $400, which gave us $320,000. And the new expenditure, which is after the tariff, is 700 units multiplied by $500. And this gave us $350,000. And the difference between the two is 350 - 320, and the answer is $30,000.

Currency pricing

The currency of Fairsea is the Fairsea dinar. The current exchange rate between the Fairsea dinar and the US dollar is $1 to 0. 35. While the rate between US dollars and the euro is 1 euro to 1. 12 US dollars. Given the above exchange rates, calculate the current exchange rate between the euro and the Fairsea dinar. This sounds quite difficult, but it is pretty straightforward. Now that we know that 1 euro is 1. 12 US dollars and we know that 1 US dollar is 0. 35 FD. Therefore, we'll take 1. 12 US dollars multiplied by 0. 35 FD. This gives us 0. 392 FD. And that is the answer.

Currency value

In January, the exchange rate was 1 US dollar to 125 KES. By December, the rate changed to 1 US dollar equals 150 KES. Calculate the percentage change in the value of the US dollar relative to the Kenyan shilling. Now, here they are asking for a percentage change. So, this is the new rate minus the old rate divided by the old rate times 100. So, the new rate in December was 150 and the old rate was 125. So, that's 150 - 125 divided by 125 * 100. So, 150 - 125 is 25 over 125 * 100 is 20% appreciation of the USD against the KES.

Current account

And final question, Albania has a current account deficit of 125 million in 2017. Calculate the value of V, exports of services for Albania in 2017. We know that on this table, the total amount of credits is the exports of goods and services. This is 1,527 plus V. And the total debits is 2,431. So, now that we know our current account is minus 125 and that equals to credits minus debits. So, simply put, our current account balance right now is 125 in deficit, which is 1,527 plus V minus 2,431. And then we find out the total money out minus the deficit, which is 2,431 minus 125, which gives us 2,306. And this is the total amount of money we actually earned. If you think about it, if you went to a store and you spent $2,431, but you look in your bank account and you're only $125 in the hole or in deficit or in debt, this means that you must have had $2,306 in your pocket when you walked in. This is essentially the same as this country. So, 2,306 is the total amount of money earned. And then we subtract the exports of goods, which is 1,527, and that gives us the answer of $779 million. I hope that helped. I hope you guys have a good day. Bye-bye.

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