Question

Suppose that you’re running a farm to produce raw chickens for KFC. You already know that a baby chick needs two bags of feed to be raised and sold as a broiler chicken.

We use ? to represent the number of broiler chickens you produce, where ?1 is the number of chicks, and ?2 is the number of bags of feed.

(1) Which type of production does the above belong to, fixed proportions, perfect substitutes, or Cobb-Douglas production? Discuss your understanding of it.

(2) Draw two isoquants in the coordinate system, for example, the isoquants ?=4 and ?=6. (8 points)

(3) Write the corresponding production function ?=?(?1,?2)= ?

Answer 1

1) This is a type of fixed proportion production function.

• This is because, from the question we can infer that x1(number of chicks) and x2(number of bags of feed) are complementary goods.
• Complementary goods - if price of one good increase then demand for other good will decrease. In our example, suppose if price of chicks increase then demand for feed bags will decrease. Thus we can say they are complementary goods.

2)

• I will explain the diagram in part 3

3) According to question : x1 = 2 (x2) and in part 1 we have seen that we have fixed proportion production function. So we can write it as -

• Y = f(x1, x2) = min (x1, 2 x2)
• Solving the equation : x1 = 2 x2
  • x2/x1 = 1/2 = slope (as seen in fig above)
• We draw isoquant (same output) as follows by using out production function equations and then finding the points
  • Isoquant Y =4 will pass through points like (4,2), (4,3), (4,4), (4,5), (5,2), (6,2) etc
    • Eg at (4,2), Y = min(4, 2*2) = 4
  • Isoquant Y=6 will pass through points like (6,3), (6,4), (6,5), (6,6), (7,3), (8,3) etc
    • Eg at (8,3), Y = min(8, 2*3)= min (8,6) = 6