Finding maximum output, profit and consumer surplus

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SUMMARY

The discussion focuses on maximizing output, profit, and consumer surplus in economic models. The short-run production function is defined as Q = L²e^(-0.01L), where Q represents output and L denotes labor. To achieve profit maximization, the condition MR = MC must be satisfied, along with the derivative conditions (MR)’ < (MC)’. Additionally, the consumer surplus is calculated using the demand function P = 100 - Q² at Q = 8.

PREREQUISITES
  • Understanding of short-run production functions
  • Knowledge of marginal revenue (MR) and marginal cost (MC) concepts
  • Ability to perform differentiation in calculus
  • Familiarity with consumer surplus calculations
NEXT STEPS
  • Study the derivation of average product of labor from the production function Q = L²e^(-0.01L)
  • Learn how to apply the first derivative test for profit maximization
  • Explore consumer surplus calculations using different demand functions
  • Investigate the implications of the second derivative test in profit maximization scenarios
USEFUL FOR

Students in economics, particularly those studying microeconomic theory, as well as professionals involved in production management and economic analysis.

CollegeGuy
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I am struggling in college at the moment and I don't know where else to turn. Any assistance or advice would help, thank you
(a)

A firm’s short-run production function is given by Q = L2e-0.01L where Q = output and
L = labour. Find the value of L that maximises the average product of labour.





(b)

Using derivatives, show that the rule for profit maximisation is:



MR = MC and (MR)’ < (MC)’



Where MR = marginal revenue and MC = marginal cost.





(c)

Find the consumer’s surplus at Q = 8 for the demand function P = 100 – Q2.
 
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CollegeGuy said:
...
(a)

A firm’s short-run production function is given by Q = L2e-0.01L where Q = output and
L = labour. Find the value of L that maximises the average product of labour...

Is this supposed to be:

$$Q=L^2-0.01L$$ ?

If so, there are several says to proceed. You could find the axis of symmetry, express in vertex form, or use differentiation. What have you tried so far?
 

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