Consider China and US in a Ricardian world. Each country produces two goods, corn andwheat. Each country has 600 units of labour hour available. The table of unit labour costs forproduction of each good in each country is below:Corn WheatChina 6 4US 2 2a. Derive China’s production possibility frontier (PPF). (Write down an equation of China’sPPF)b. Draw China’s PPF. Have the quantity of corn on the horizontal axis.(Derive US’sproduction possibility frontier (PPF). (Write down an equation of US’s PPF)c. Draw US’s PPF.Have the quantity of corn on the horizontal axis.d. Derive US’s production possibility frontier (PPF). (Write down an equation of China’sPPF)e. What is the slope of PPF of China? Explain your answer.f. What is the slope of PPF of US? Explain your answer.g. In the absence of trade, what would be the prices of corn in terms of wheat in China?
Question
Consider China and US in a Ricardian world. Each country produces two goods, corn andwheat. Each country has 600 units of labour hour available. The table of unit labour costs forproduction of each good in each country is below:Corn WheatChina 6 4US 2 2a. Derive China’s production possibility frontier (PPF). (Write down an equation of China’sPPF)b. Draw China’s PPF. Have the quantity of corn on the horizontal axis.(Derive US’sproduction possibility frontier (PPF). (Write down an equation of US’s PPF)c. Draw US’s PPF.Have the quantity of corn on the horizontal axis.d. Derive US’s production possibility frontier (PPF). (Write down an equation of China’sPPF)e. What is the slope of PPF of China? Explain your answer.f. What is the slope of PPF of US? Explain your answer.g. In the absence of trade, what would be the prices of corn in terms of wheat in China?
Solution
a. To derive China's production possibility frontier (PPF), we need to consider the unit labor costs for producing corn and wheat in China. The unit labor cost for corn in China is 6, and for wheat, it is 4. Since China has 600 units of labor hour available, we can calculate the maximum quantity of corn and wheat that China can produce by dividing the total labor hour by the unit labor cost for each good.
Let's denote the quantity of corn as C and the quantity of wheat as W. The equation for China's PPF can be written as:
6C + 4W = 600
b. To draw China's PPF, we need to plot the combinations of corn and wheat that satisfy the equation derived in part a. The quantity of corn will be on the horizontal axis, and the quantity of wheat will be on the vertical axis.
c. To derive the US's production possibility frontier (PPF), we need to consider the unit labor costs for producing corn and wheat in the US. The unit labor cost for both corn and wheat in the US is 2. Using the same approach as in part a, we can calculate the maximum quantity of corn and wheat that the US can produce.
Let's denote the quantity of corn as C' and the quantity of wheat as W'. The equation for US's PPF can be written as:
2C' + 2W' = 600
d. To draw US's PPF, we need to plot the combinations of corn and wheat that satisfy the equation derived in part c. The quantity of corn will be on the horizontal axis, and the quantity of wheat will be on the vertical axis.
e. The slope of China's PPF can be calculated by taking the ratio of the change in wheat quantity to the change in corn quantity. Since the equation for China's PPF is 6C + 4W = 600, we can rearrange it to solve for W in terms of C:
W = (600 - 6C) / 4
The slope of China's PPF is the coefficient of C, which is -6/4 or -1.5. This means that for every unit increase in corn production, China has to give up 1.5 units of wheat production.
f. The slope of US's PPF can be calculated in a similar way. Since the equation for US's PPF is 2C' + 2W' = 600, we can rearrange it to solve for W' in terms of C':
W' = (600 - 2C') / 2
The slope of US's PPF is the coefficient of C', which is -2/2 or -1. This means that for every unit increase in corn production, the US has to give up 1 unit of wheat production.
g. In the absence of trade, the prices of corn in terms of wheat in China would be determined by the opportunity cost of producing corn. From the PPF equation for China (6C + 4W = 600), we can rearrange it to solve for W in terms of C:
W = (600 - 6C) / 4
The price of corn in terms of wheat would be the coefficient of C, which is 6/4 or 1.5. This means that in China, the price of corn would be 1.5 times the price of wheat.
Similar Questions
Consider China and US in a Ricardian world. Each country produces two goods, corn andwheat. Each country has 600 units of labour hour available. The table of unit labour costs forproduction of each good in each country is below:Corn WheatChina 6 4US 2 2a. 1) What is the marginal product of labour in corn in China?2) What is the opportunity cost of producing corn in China?b. 1) What is the marginal product of labour in wheat in China?2) What is the opportunity cost of producing wheat in China?c. 1) What is the marginal product of labour in corn in US?2) What is the opportunity cost of producing corn in US?d. 1) What is the marginal product of labour in wheat in US?2) What is the opportunity cost of producing wheat in US?e. Which country has absolute advantage in corn?f. Which country has absolute advantage in wheat?g. Which country has comparative advantage in corn?h. Which country has comparative advantage in wheat?
Consider Home and Foreign in a Ricardian world (includes all the assumptions of the Ricardianmodel). Each country produces two goods, wine and cotton. Each country has 4,800 labour hoursavailable. The accompanying table shows the number of hours required to produce one unit ofeach good in each country. Answer the following questions using the information given by thetable:a. What is the opportunity cost of cotton in each country? Show your work.b. Draw the graph of the production possibility frontier (PPF).c. Which country has an absolute advantage in Wine? Explain your answer.d. Which country has a comparative advantage in Wine? Show your work and explain your answer.e. Which good does each country produce and export when the equilibrium international relativeprice of wine in terms of cotton is 1?f. Suppose the equilibrium international relative price of wine in terms of cotton is 1. Draw the graphof the production possibility frontier (PPF) for each country when they trade. Show how the twocountries can benefit from free trade. Explain your answer and fully label your graph to get marks.g. Draw the world relative supply (RS) of wine. Fully label your graph to get marks (Do not drawthe world relative demand (RD) of wine yet).h. Now, suppose that the world relative demand is drawn such that the equilibrium internationalrelative price of wine is at 1. Draw the world relative demand curve of wine on the diagram above(in part g). Explain which country (countries) benefit(s) (most) from free trade in this case.i. Now, suppose that the world relative demand is drawn such that the equilibrium internationalrelative price of wine is at 1.25 (=5/4). Draw the world relative demand curve of wine on thediagram above (in part g). Explain which country (countries) benefit(s) (most) from free trade inthis case.j. Calculate Home country’s relative productivity of labour in each sector.k. Suppose that the price of wine is $10 per bottle and the price of cotton is $10 per bushel. Calculatethe relative wage in Home (the wage of Home relative to the wage in Foreign). Show your workand explain your answer.l. Show the relative wage in Home lies in between the relative productivity of labour of two sectorsusing the information you obtained from parts j and k.Wine CottonHome 6 8Foreign 5 4
Consider a production possibilities frontier (PPF) with Good X on the horizontal axis and Good Y on the vertical axis. The slope of the PPF tells us the _____ of producing one additional unit of Good X.Multiple choice question.profitabilitytotal costaverage costopportunity cost
The production possibility frontier shows the maximum output a nation can produce with available resources.Group of answer choicesTrueFalse
The production possibilities frontier (PPF) shows how much of two goods an economy can produce when it is using all available as efficiently as possible.
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