7. A firm is using 20 units of labor and 30 units of capital to produce 4,000 un
ID: 1110753 • Letter: 7
Question
7. A firm is using 20 units of labor and 30 units of capital to produce 4,000 units of output. At this combination the marginal product of labor is 50 and the marginal product of capital is 40. The price of labor is $30 and the price of capital is $20.
If answer is numerical please go to two decimal spaces.
(a) The MP per dollar is ___________ and the MP per dollar of capital is ______________.
(b) The firm can increase capital by one unit and decrease labor by _________________ units while keeping cost constant.
(c) The maximum output at the given cost the firm will increase ________________ (enter labor or capital) and decrease ________________ (enter labor or capital) until the MRTS equals _______________.
8. For each of the following, describe return to scale.
A. Q = K + L
B. Q = K ½ L ½
C. Q = K2L
Function _____________ (enter A, B, or C) exhibits increasing returns to scale.
Function _____________ (enter A, B, or C) exhibits constant returns to scale.
Function _____________ (enter A, B, or C) exhibits decreasing returns to scale.
Explanation / Answer
Question 7
(a)
MPL = 50
PL = 30
MP per dollar of labor = MPL/PL = 50/30 = 1.67
MPK = 40
PK = 20
MP per dollar of capital = MPK/PK = 40/20 = 2
The MP per dollar of labor is 1.67 and the MP per dollar of capital is 2.
(b)
Ratio of input prices = PK/PL = 20/30 = 0.67
This indicates that if capital is increased by 1 unit then labor has to be decreased by 0.67 units in order to keep the cost constant.
The firm can increase capital by one unit and decrease labor by 0.67 units while keeping cost constant.
(c)
MPL/PL = 50/30 = 1.67
MPK/PK = 40/20 = 2
MPL/PL < MPK/PK
So,
The maximum output at the given cost the firm will increase labor and decrease capital until the MRTS equals ratio of input prices.
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