Question

George produces computer software (user friendly). His firm's production function is Q = 1K + 2L, where Q is the programs, K is capital employed, and L is the labour used.

If George faces factor prices of Pk=1 and Pl =1, the cheapest way to produce Q = 60 is:

Part 1: By using how many units of capital?  

Part 2: By using how many units of labour?  

If George faces factor prices of Pk=2 and Pl=6, the cheapest way to produce Q = 60 is

Part 3: By using how many units of capital?  

Part 4: By using how many units of labour?  

Answer 1

Q= k + 2L

MPL = 2 ; MPK = 1

MRS = 2/1= 2

PL/PK = 1/1= 1

Because MRS is greater than price ratio, only L should be used.

1. Capital = 0

2. Labor = 60/2= 30 units

Now, PL/PK = 6/2= 3

Because MRS is less than price ratio, only K should be used.

3.Capital = 60

4. Labor = 0