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    Okay if you have capital and labour as perfect substitutes where:

    3 units of labour equals 1 unit of capital

    And the prices are:

    Labour = $1
    Capital = $4

    Which of the following will the firm pick?

    a- employ only capital
    b- employ only labour
    c- three times as much capital as labour
    d- four times as much labour as capital

    Why?
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    b)

    call your production function: q = L + 3K. that is to produce 3 units you need 3 units of labor or 1 unit of capital. if you have Labor on the horizontal axis put a point at 3, and if capital on vertical then put a point at 1. draw a straight line. that is the contour for q = 3. Now add the isocost line. What does it cost to have 3 units of labor? It costs 3. how much capital can you get for 3 dollars? 3/4 capital. so draw a straight line from 3 to 3/4.

    You see that the isocost line is shallower than the production contour. Hence you produce at the point where the two meet which is at Labour only.

    Note: if say capital would have cost $2 then you would only produce capital. In this case the iso cost line is steeper and so for the given production contour, the lowest cost is where the iso cost line (now slope 1/2) still meets the production contour is at capital only.

    General rule for perfect substitutes: q = ax + by (in your case a =1 and x is labour, b is 3 and y is capital)

    if w1 is price of x and w2 is price of y then

    if w1/w2 < a/b (both in absolute value) you take take x only and vice versa

    Hard to explain without a diagram so draw it to see it for yourself.
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    (Original post by danny111)
    b)

    call your production function: q = L + 3K. that is to produce 3 units you need 3 units of labor or 1 unit of capital. if you have Labor on the horizontal axis put a point at 3, and if capital on vertical then put a point at 1. draw a straight line. that is the contour for q = 3. Now add the isocost line. What does it cost to have 3 units of labor? It costs 3. how much capital can you get for 3 dollars? 3/4 capital. so draw a straight line from 3 to 3/4.

    You see that the isocost line is shallower than the production contour. Hence you produce at the point where the two meet which is at Labour only.

    Note: if say capital would have cost $2 then you would only produce capital. In this case the iso cost line is steeper and so for the given production contour, the lowest cost is where the iso cost line (now slope 1/2) still meets the production contour is at capital only.

    General rule for perfect substitutes: q = ax + by (in your case a =1 and x is labour, b is 3 and y is capital)

    if w1 is price of x and w2 is price of y then

    if w1/w2 &lt; a/b (both in absolute value) you take take x only and vice versa

    Hard to explain without a diagram so draw it to see it for yourself.
    Thanks, really helpful..
 
 
 
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