a) (5 points) Fill in the Table below. Number of workers Units of output MPN 0 0
ID: 1134435 • Letter: A
Question
a) (5 points) Fill in the Table below.
Number of workers
Units of output
MPN
0
0
1
20
2
38
3
53
4
66
5
77
6
86
7
93
b. (10 points) Define the marginal product of labor and explain how it relates to the production function (with N on horizontal axis and Y on vertical axis). What shape does a production function typically take and why? Does this production function take the 'typical' shape?
c) (10 points) You can hire all the workers you want at $100 per worker. The price of your product is $10. Calculate the number of workers that you will hire and the associated profit in REAL terms (as we did in class, we 'assume away' all other costs of production). Please give me the marginal REAL profit of each worker hired and then add them up and that is the total profit in real terms.
d)(10 points) Suppose, due to an increase in the capital stock (K), the marginal productivity of each worker rises by 2. Redo part c, that is, calculate the number of workers that you will hire and the associated profit in REAL terms. Please give me the marginal REAL profit of each worker hired and then add them up and that is the total profit in real terms.
e).(10 points) Given the change in conditions and tight labor markets, you decide give each worker a raise so that the new wage is $110 (this is along with the increase in productivity) . Now calculate the number of workers that you will hire and the associated profit in REAL terms. Please give me the marginal REAL profit of each worker hired and then add them up and that is the total profit in real terms. Hint, if you break even on the last worker hired then you still hire them.
.
f) (10 points) Are workers better or worse off and why? Are firms better or worse off and why. What has happened to personal income tax revenue and why?
Number of workers
Units of output
MPN
0
0
1
20
2
38
3
53
4
66
5
77
6
86
7
93
Explanation / Answer
(a) MPN = Change in output (Q) / Change in Workers (N)
(b) Marginal product of labor (MPN) is the increase in output resulting from an additional unit of labor hired. In the N-Y plane, when production initially increases, total product (TP) initially increases, and MPN initially increases. Then TP starts increasing at a decreasing rate and MPN starts to fall. When production (TP) is maximum, MPN is zero, and when production starts falling, MPN is negative.
The production function typically is inverse-U shaped. It initially increases at an increasing rate, then starts increasing at a decreasing rate, reaches a maximum, and then starts decreasing. In this case, the production function has the typical shape.
(c) Hiring is optimal when (Output price x MPN) = Wage rate
$10 x MPN = $100
MPN = 10
From above table, closest value of MPN is 11 when N = 5. So, 5 workers will be hired with Q = 77.
Profit ($) = Revenue - Cost = (Output price x Q) - (Wage rate x N) = (10 x 77) - (5 x 100)
= 770 - 500 = 270
(d) When MPN rises by 2 units at every level, closest value of MPN will be 11 (= 9 + 2) when N = 6 and Q = 86. Therefore,
Profit ($) = (86 x 10) - (6 x 100) = 860 - 600 = 260
NOTE: As per Chegg Answering policy, first 4 parts have been answered.
N Q MPN 0 0 1 20 20 2 38 18 3 53 15 4 66 13 5 77 11 6 86 9 7 93 7Related Questions
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