1/2 1/212 A firm\'s production function using capital (K) and labor (L) is f(L,K

Question

1/2 1/212 A firm's production function using capital (K) and labor (L) is f(L,K)-(LK). How many of the following statements are true concerning its Marginal Rate of Technical Substitution? If the firm has 16 units of labor and 4 units of capital, it would be willing to trade inputs at a rate of 2 units of labor to 1 unit of capital. If the firm has 25 units of labor and 1 units of capital, the (negative of) the slope of the isoquant K=f(L) is 5. If the firm has 64 units of labor and 25 units of capital, it would be willing to trade inputs at a rate of 8 units of labor to 5 units of capital. A. 1 B. 2 C. 3 D. None of the above statements are true.

Explanation / Answer

Consider the given problem, here according to the production function given the “MRTS” is given by, “MRTS = (K/L)^1/2”.

So, if L=16 and K=4, => MRTS=(4/16)^1/2=1/2.

So, which implied, if we increase “L” by 1 unit we need to decrease “K” by “1/2”, to fixed the level of output.

=> If we increase “L” by 2 units we need to decrease “K” by “1/2*2=1”, to fixed the level of output.

=> the 1st statement is TRUE.

Now, MRTS=(K/L)^1/2, => if L=25 and K=1, => (K/L)^1/2=(1/25)^1/2=1/5.

So, the 2nd statement is FALSE.

Now, the MRTS=(K/L)^1/2, if L=64 and K=25, =>(K/L)^1/2=(25/64)^1/2=5/8.

So, which implied, if we increase “L” by 1 unit we need to decrease “K” by “5/8”, to fixed the level of output.

=> If we increase “L” by 8 units we need to decrease “K” by “5/8*8=5”, to fixed the level of output.

=> the 3rd one is TRUE.

So, the correct option is “B=2”

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