a)
To ascertain:The
a)
Answer to Problem 10.6P
The production possibility curve for region A
The production possibility curve for region B
Explanation of Solution
To calculate the production possibility curves for region A, consider the following production
function for region A:
Here, Ix, is the labor allocated in the production of good x and I, is the labor allocated in the
production of good y
The total amount of labor available to region A is 100, that is,
From the production function, compute the value of Ixand Iy, as follows:
Now, substitute the value of Ix, and Iy, in the equation of total available labor and compute the
production function as follows:
Hence, the production for region
The PPF curve for region A is shown below:
In this graph the vertical axis shows production of good y and horizontal axis shows production of good x.
To calculate the production possibility curves for region B, consider the following production
function for region B:
Here, Ixis the labor allocated in the production of good x and Iyis the labor allocated in the
production of good y .
The total amount of labor available to region A is 100, that is,
From the production function, compute the value of Ix and Iyas follows:
Now, substitute the value of Ix and Iy and in the equation of total available labor and compute theproduction function as follows:
Hence, the production of region B is
The PPF curve for region B is shown below:
In the above graph, the vertical axis shows the production of good y and the horizontal axisshows the production of good x.
Introduction: Production possibilities of frontier is referring to specify the highest production combination of two products or services by the fixed amount of investment.
b)
To ascertain:conditions behind work allotted in region A and B.
b)
Answer to Problem 10.6P
The condition must hold for production allocation in country R between regions is
Explanation of Solution
To allocate the production efficiently in a region, the rate of production transformation (RPT) mustbe equal to the marginal rate of substitution (MRS).
Mathematically, the following condition musthold:
To allocate the production of two goods efficiently in the region A, the following condition musthold:
Hence, the rate of production transformation (RPT) in region A is
To allocate the production of two goods efficiently in region B, the following condition must hold:
Hence, the rate of production transformation (RPT) in region B is
To achieve the production
Hence, the condition must hold for production allocation in country R between regions is
Introduction: The marginal rate of production transformation is can be described as number of quantity of product that inevitable in order to attain a unit of another product.
c)
To ascertain:production possibility curve for a country.
c)
Answer to Problem 10.6P
The PPF for a country R is shown below:
Explanation of Solution
To determine the combined PPF for a country R,
first, calculate the combine production function asfollows:
Region A
Region B
Equate the Ix , and Iy , as follows:
Combine production function is shown below:
Thus, the combined PPF is
The total output of x is 12. Substitute the value of x in the above combined PPF and calculate the
output of y as follows:
Hence, the total output of y produced in a country is 9
The PPF for a country is shown below:
Introduction: Production possibilities of frontier is referring to specify the highest production combination of two products or services by the fixed amount of investment.
d)
To ascertain:production possibilities frontier for whole country.
d)
Answer to Problem 10.6P
If the labor is mobile within the country the production can be increased by allocating the resources in the favor of the more productive region.
Explanation of Solution
The PPF for the whole country can be developed for the whole country in the same way the PPF has been calculated for country R with two regions
If the labor is mobile within the country the production can be increased by allocating the resources in the favor of the more productive region.
Introduction: Production possibilities of frontier is referring to specify the highest production combination of two products or services by the fixed amount of investment.
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Chapter 10 Solutions
EBK INTERMEDIATE MICROECONOMICS AND ITS
- Consider two countries (Home and Foreign) that produce goods 1 (with labor and capital) and 2 (with labor and land). Initially, both countries have the same supply of labor (250 units each), capital, and land. The capital stock in Home then grows. This change shifts out both the production curve for good 1 as a function of labor employed and the associated marginal product of labor curve. Nothing happens to the production and marginal product curves for good 2. a. Show how the increase in the supply of capital for Home affects its production possibility frontier. Using the three-point curved line drawing tool, draw a new PPF for Home that reflects the increase in the supply of capital. Properly label the curve. Carefully follow the instructions above and only draw the required object. Output of good 2 250 Home 250 PPF0 Output of good 1 Qarrow_forwardA country (Country X) that only produces two goods (good A) and (good B) in a closed market with another country (Country Y) that only produces the same two goods. Country X has 1000 workers and Country Y has 4000 and no workers can migrate. It takes Country X 2 workers to produce good A and 3 workers to produce good B whereas it takes Country Y 3 workers to produce good A and 1 worker to produce good B. Labour is the only factor of production and both follow a standard Ricardian model that has an identical utility function. Country X decides to adopt an import substitution strategy to improve the efficiency of productivity of good B. Explain what this means and provide an opinion on this strategy?arrow_forwardConsider two competitive economies that have the same quantities of labor (L = 400) and capital (K = 400), and the same technology (A = 100). The economies of the countries are described by the following Cobb–Douglas production functions: North Economy: Y = A L0.3K0.7 South Economy: Y = A L0.7K0.3 In which economy is the marginal product of labor larger? Explain.arrow_forward
- Heckscher-Ohlin: Consider an economy with two goods (corn and potatoes), both produced using capital and labor. Both factors can freely move across sectors. The technologies for the two sectors are given by the following Cobb-Douglas production functions:arrow_forwardSuppose two economies Home (H) and Foreign (F) produce two goods, bread and wine, with only one production factor: labour. Production technology, expressed as marginal product of labour (MPL), is given in the following table: Technologies expressed as MPL Bread Wine Home 1/6 1/12 Foreign 1/4 1/2 Suppose that Home has 2400 units of labour and Foreign has 1800 units of labour. a. ) Derive the Production Possibilities Frontier (PPF) and the Consumption Possibility Frontier (CPF) for Home and Foreign, with bread on the horizontal axis and wine on the vertical axis. What is the autarky equilibrium price of bred relative to wine in each country? b.) What country has the absolute advantage in producing each good? What country has the comparative advantage in producing each good? Briefly explain the difference between these two concepts. Suppose both countries are now free to trade. The world relative price of bread is 1. c. What is the pattern of specialisation and trade?…arrow_forwardNation alpha can produce either 3 units of good X or 1 unit of good Y with 1 hour of labour whereas nation beta can produce either 4 units of good X or 2 units of good Y with one hour of labor . Assuming that labor is the only input then ?arrow_forward
- On a certain small island, there are only 100 units of labour (L) and 200 units of capital (K) available. Two commodities can be produced on this island, A and B. The production function for commodity A is given by QA given by QB = min (LB, KB). Find the production possibilities frontier for this island. Illustrate the production possibilities set for this island. min (LA, () KA). The production function for commodity B isarrow_forwardHeckscher-Ohlin: Consider an economy with two goods (cornand potatoes), both produced using capital and labor. Both factors can freely move across sectors. The technologies for the two sectors are given by the following Cobb-Douglas production functions:arrow_forwardConsider a specific-factors model where two Countries, Denmark and Tanzania, use labor to produce cake (C) and helicopters (H). However, arable land (A) are a factor specific to cake, and jerrycans (J) are a factor specific to helicopters. Suppose that Tanzania has L = 100 workers, J = 40 jerrycans, and A = 1000 arable land. The production functions and marginal products of labor for cake and helicopters are: C = 4 x Lc %D 0.5 x A0.5 MPLC = 2 x Lc0.5 x A0.5 H = 4 x LH0.5 x J0.5 MPLH = 2 x LH-0.5 x J0.5 In Tanzania, the price of crystals is 20 and the price of hyperdrives is 200. In this case, the wage rate will be ___ and the cake industry and will be employed in the helicopter industry. %3D workers will be employed in workersarrow_forward
- Consider a specific-factors model where two Countries, Denmark and Tanzania, use labor to produce cake (C) and helicopters (H). However, arable land (A) are a factor specific to cake, and jerrycans (J) are a factor specific to helicopters. Suppose that Tanzania has L = 100 workers, J = 40 jerrycans, and A = 1000 arable land. The production functions and marginal products of labor for cake and helicopters are: C = 4 x Lc0.5 x A0.5 MPLc = 2 x Lc-0.5 x A0.5 H = 4 x LH0.5 x J0.5 MPLH = 2 x LH-0.5 x J0.5 In Tanzania, the price of crystals is 20 and the price of hyperdrives is 200. In this case, the wage rate will be ________ and ________ workers will be employed in the cake industry and __________ workers will be employed in the helicopter industry.arrow_forwardConsider an economy with two goods, cloth and food. The production possibility frontier of this economy is given by Q, +Q = 8000. Preferences of the consumers are described by the following utility function U(Qc,Q;) =/Q.QF: Suppose this economy can trade with the rest of the world at the relative price of cloth to food equal 2. How much food will this economy import?arrow_forwardSuppose there exist two imaginary countries, Sequoia and Denall. Their labor forces are each capable of supplying four million hours per week that can be used to produce almonds, shorts, or some combination of the two. The following table shows the amount of almonds or shorts that can be produced by one hour of labor. Almonds Country (Pounds per hour of labor) Sequoia Denall Suppose that initially Denall uses 1 million hours of labor per week to produce almonds and 3 million hours per week to produce shorts, while Sequoia uses 3 million hours of labor per week to produce almonds and 1 million hours per week to produce shorts. As a result, Sequola produces 12 million pounds of almonds and 16 million pairs of shorts, and Denall produces 6 million pounds of almonds and 36 million pairs of shorts. Assume there are no other countries willing to engage in trade, so, in the absence of trade between these two countries, each country consumes the amount of almonds and shorts it produces.…arrow_forward