I have the answers but I need an explanation on how to do the math: Shoes come i
ID: 1206648 • Letter: I
Question
I have the answers but I need an explanation on how to do the math:
Shoes come in pairs: A left (foot) shoe has to find a right (foot) shoe. A representative worker in the North can produce EITHER 30 right shoes OR 10 left shoes (or any convex combination of these figures). There are 10 workers living in the North. A representative worker in the South can produce either 1 right shoe or 3 left shoes (or any convex combination of these figures). There are 100 workers in the South.
QUESTIONS: (I) How many pairs of shows the North will produce in the case of aurtarky (no trade)? And how many pairs of shoes the South will produce under no trade?
The North will produce 75 right foot shoes and 75 left foot shoes allocating 2.5 workers to produce right shoes (2.5x30=75) and 7.5 workers to produce left foot shoes (7.5x10=75) and 2.5+7.5=10. The South will produce 75 left foot shoes and 75 right foot shoes allocating 25 workers to produce left shoes (25x3=75) and 75 workers to produce 75 right foot shoes (75x1=75).
(II) Suppose that these two areas open up to trade and one right shoe can be exchanged for one left shoe. How may pairs of shoes will the North consume? And the South? The north will specialize in the right shoe production allocating all work to produce 300 right foot shoes. The South will specialize in the left shoe production producing 300 left foot shoes. Then they can trade one for one shoe and consume 150 pairs each.
(III) Suppose now that population in the South increases to 1000 workers. What would be the new exchange rate for right/left shoes and how many pair of shoes the North will be consuming? The terms of trade are those of the South: One right shoe can get three left shoes. Hence, the North will produce 300 right shoes. As discussed in class the North will be consuming 225 pairs. The consumption in the South is the same as in autarky and can be inferred from part 1. That is the South will consume 750 pairs.
Explanation / Answer
Answer (i):
For North : Given A representative worker in the North can produce EITHER 30 right shoes OR 10 left shoes
Let us assume x worker produce Right Shoe. Since total number of worker is 10, hence number of worker working on left show will be = 10-x.
Now total number of right shoe produced = 30 * x
Total number of Left shoe produced = 10 * (10-x)
For optimum solution number of left shoe should be equal to right shoe.
Hence, 30x = 100 - 10x
So, 40x = 100, hence x = 100/40 = 2.5
So number of workers working on right shoe = x = 2.5
Number of workers working on left shoe = 10 - x = 7.5
For South : A representative worker in the South can produce either 1 right shoe or 3 left shoes (or any convex combination of these figures). There are 100 workers in the South
Let us assume x worker produce Right Shoe. Since total number of worker is 100, hence number of worker working on left show will be = 100-x.
Now total number of right shoe produced = 1 * x
Total number of left shoe produced = 3 * (100-x)
For optimum solution number of left shoe should be equal to right shoe.
Hence, x = 300 - 3x
So, 4x = 300, hence x = 300/4 = 75
So number of workers working on right shoe = x = 75
Number of workers working on left shoe = 100 - x = 25
Answer (ii):
Let us assume x worker produce Right Shoe in North. Since total number of worker is 10, hence number of worker working on left shoe in North will be = 10-x.
Let us assume y worker produce Right Shoe in South. Since total number of worker is 100, hence number of worker working on left shoe in South will be = 100-y.
Now total number of right shoe produced in North = 30 * x
Total number of left shoe produced in North = 10 * (10-x)
Now total number of right shoe produced in South= 1 * y
Total number of left shoe produced in South = 3 * (100-y)
So total right shoe = 30x + y
Total left shoe = 100-10x + 300 -3y
Hence 30x + y = 400 -10x - 3y
That means : 40x + 4y = 400
That means 10x + y = 100
Now to maximize this, x which is right shoe for North should be equal to 10 (total number of worker in north). Since right shoe producer are more efficient in north
Hence 10*10 + y = 100 That means y = 0.
So total right shoe = 30 * 10 = 300
Total left shoe = 3 * (100-0) = 300
Answer (iii):
Let us assume x worker produce Right Shoe in North. Since total number of worker is 10, hence number of worker working on left shoe in North will be = 10-x.
Let us assume y worker produce Right Shoe in South. Since total number of worker is 1000, hence number of worker working on left shoe in South will be = 1000-y.
Now total number of right shoe produced in North = 30 * x
Total number of left shoe produced in North = 10 * (10-x)
Now total number of right shoe produced in South= 1 * y
Total number of left shoe produced in South = 3 * (1000-y)
So total right shoe = 30x + y
Total left shoe = 100-10x + 3000 -3y
Hence 30x + y = 3100 -10x - 3y
That means : 40x + 4y = 3100
That means 10x + y = 775
Now to maximize this, x which is right shoe for North should be equal to 10 (total number of worker in north). Since right shoe producer are more efficient in north
Hence 10*10 + y = 775 That means y = 675.
So total right shoe in north = 30 * 10 = 300
Total right shoe in south = 1 * y = 675
Total left shoe in South = 3 * (1000-675) = 3 * 325 = 975
Total right shoe = 975
Total left shoe = 975