Question

In: Finance

Local chain of sandwich shops sells sandwiches in a competitive market at $5.39 each. The hourly...

Local chain of sandwich shops sells sandwiches in a competitive market at $5.39 each. The hourly production function is:

Q = 136L - L2

The marginal product of labor function is:

MPL = 136 - 2L

If the competitive hourly wage is $14.68

a) how many employees do they hire?

b) what are the total hourly labor costs for the firm?

c) what is the total output of the firm?

d) what is the total revenue of the firm?

Solutions

Expert Solution

Formula sheet

A B C D E F G H
2
3 Q= 136L-L2
4 MPL = 136-2L
5
6 a)
7
8 The maximum output will be where the marginal product of labor function is zero i.e.
9 136-2L = 0
10
11 Solving the above euation
12 L= =136/2 =136/2
13
14 Thus number of enpmloyees to be hired is =D12
15
16 b)
17
18 Hourly wage 14.68
19 Number of Labors =D14
20 Total hourly labor costs =D18*D19 =D18*D19
21
22 Hence Total hourly labor costs =D20
23
24 c)
25
26 Total output of the firm can be calculated using hourly production function.
27 Q= 136L-L2
28 Q= 136*68-682
29
30 Q= =136*68-68^2 =136*68-68^2
31
32 Hence total output of the firm is =D30
33
34 d)
35
36 Price per units 5.39
37 Number of units produced =D32
38 Total Revenue =D36*D37 =D36*D37
39
40 Hence total revenue of the firm is =D38
41

jeff jeffy answered 1 year ago
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