Answer:
[tex]L + 2K = 200[/tex]
Step-by-step explanation:
Given
[tex]E=1000[/tex] --- Expenditure
[tex]L=200[/tex] --- Labor
[tex]K = 100[/tex] --- Capital
Required
Determine the budget line
First, we calculate the units of labor
[tex]U_1 = \frac{E}{L}[/tex]
[tex]U_1 = \frac{1000}{200}[/tex]
[tex]U_1 = 5[/tex]
Next, the units of capital
[tex]U_2 = \frac{E}{K}[/tex]
[tex]U_2 = \frac{1000}{100}[/tex]
[tex]U_2 = 10[/tex]
The budget line equation is:
[tex]U_1 * L + U_2 * K = E[/tex]
At this point, we take L and K as variables.
So, the equation becomes
[tex]5* L + 10* K = 1000[/tex]
[tex]5 L + 10K = 1000[/tex]
Divide through by 5
[tex]L + 2K = 200[/tex] -- Budget line equation
