S1. A firm's production function is well described by the equation Input prices are $10 per labor hour and $20 per machine hour, and the firm sells its output at a fixed price of $10 per uni a. In the short run, the firm has an installed capacity of K = 50 machine hours per day, and this capacity cannot be varied. Create a spreadsheet (based on the example below) to model this production setting. Determine the firm's profit-maximizing employment of labor. Use the spreadsheet to probe the solution by hand before using your spreadsheet's optimizer. Confirm that MRPL = MCL. A C D 1 2 3 4 5 6 7 8 9 10 11 B Labor MPL Q = 2L - .01L² + 3K - .02K². 20.0 1.600 OPTIMAL INPUTS MRPL 16.0 MCL 10.0 E Capital MPK F 50.0 1.000 MRPK 10.0 MCK 20.0 G H Output Price I Cost Ave Cost 136.0 10.0 MR 10.0 Revenue 1360.0 1200.0 8.8

S1. A firm's production function is well described by the equation Input prices are $10 per labor hour and $20 per machine hour, and the firm sells its output at a fixed price of $10 per uni a. In the short run, the firm has an installed capacity of K = 50 machine hours per day, and this capacity cannot be varied. Create a spreadsheet (based on the example below) to model this production setting. Determine the firm's profit-maximizing employment of labor. Use the spreadsheet to probe the solution by hand before using your spreadsheet's optimizer. Confirm that MRPL = MCL. A C D 1 2 3 4 5 6 7 8 9 10 11 B Labor MPL Q = 2L - .01L² + 3K - .02K². 20.0 1.600 OPTIMAL INPUTS MRPL 16.0 MCL 10.0 E Capital MPK F 50.0 1.000 MRPK 10.0 MCK 20.0 G H Output Price I Cost Ave Cost 136.0 10.0 MR 10.0 Revenue 1360.0 1200.0 8.8

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

S1. A firm's production function is well described by the equation
Input prices are $10 per labor hour and $20 per machine hour, and the firm sells its output at a fixed price of $10 per unit.
a. In the short run, the firm has an installed capacity of K = 50 machine hours per day, and this capacity cannot be
varied. Create a spreadsheet (based on the example below) to model this production setting. Determine the firm's
profit-maximizing employment of labor. Use the spreadsheet to probe the solution by hand before using your
spreadsheet's optimizer. Confirm that MRPL = MCL.
C
1
2
3
4
5
6
7
8
9
10
11
12
13
A
B
Labor
MPL
Q = 2L .01L² + 3K-.02K².
20.0
1.600
MRPL
16.0
MCL 10.0
D
OPTIMAL INPUTS
E
F
Capital 50.0
MPK
1.000
MRPK 10.0
MCK 20.0
G
H
Output
Price
MR
Revenue
Ave Cost
I
Profit
136.0
10.0
Cost 1200.0
8.8
10.0
1360.0
160.0
b. In the long run, the firm seeks to produce the output found in part (a) by adjusting its use of both labor and capital.
Use your spreadsheet's optimizer to find the least-cost input amounts. (Hint: Be sure to include the appropriate
output constraint for cell 13.)

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Suppose that the production function takes the form X = min(10L, 5K) and that a competitive firm faces a wage rate of £60 per week and a weekly capital rental of £32. (a) How much must the firm spend to produce 100 units of output, and what is the average cost of production when X = 100? (b) What is the incremental cost of producing the 101st unit of output? (c) What happens to the cost of producing 100 units of output if the wage rate and the rental cost of capital rise by 25 per cent each? What happens to the average and marginal cost? (d) What happens to the cost of producing 100 units of output if the wage rate increases by £1, or if the cost of capital increases by £1?