Question

ssume a particular task can be carried out by either (i) high-skilled (

L

H

) or (ii) low-skilled (

L

L

)

workers - these inputs are perfectly substitutable. Consider that high-skilled workers are twice as

productive as low-skilled workers:

q

= 2

L

H

+ 1

L

L

.

a. [2 marks] Depict the isoquant

b. [2 marks] Assume the wage rate for high-skilled labour is $100 per day and for low-skilled, it

is $60 per day. Depict the iso-cost lines

c. [1 mark] What is the pro t maximizing input choice?

Answer 1

a. If we are considering one unit of this task which can be done LH and LL according to the production function

q = 2LH + 1LL, since each LH can be replaced by 2LL and each LL can be replaced by 2LH, we can see that the isoquant would be:

q = 2*2LL + 1LL = 5LL

or

q = 2LH + 1/2LL = 2.5LH

or any combination in between

b. Isocost line depicts combinations of inputs with the same cost. In this case since the cost ratio is 0.6, i.e., $60/$100 between LL and LH, we can employ 1/0.6 of LL for each LH we want to replace

c. The graph below shows the Isoquant and Isocost on the same graph. We can see that the profit maximizing input choice (combination) is all LH

Units of LH are on vertical axis and of LL on horizontal axis. Blue line is Isoquant, and the orange and grey ones Isocost. You will see that the lower Isocost (implying lower cost) meets Isoquant when LH = 2.5 and LL = 0. It makes no sense to go with teh higher isocost which has any units of LL, and any lower isocost won't be able to produce the desired output (q)