Finding maximum output, profit and consumer surplus

In summary, the conversation is about a student struggling in college and seeking assistance or advice. The following content includes three parts: (a) a question about finding the value of labor that maximizes the average product of labor in a firm's short-run production function, (b) a rule for profit maximization using derivatives, and (c) finding consumer's surplus at a specific demand level.
  • #1
CollegeGuy
1
0
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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  • #2
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:

\(\displaystyle Q=L^2-0.01L\) ?

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?
 

Related to Finding maximum output, profit and consumer surplus

1. What is the difference between maximum output and maximum profit?

Maximum output refers to the highest level of production that a company can achieve with the given resources. Maximum profit, on the other hand, is the point at which the company's revenue is equal to its costs. This can occur at a level of output that is lower than the maximum output, as it takes into account the costs of production.

2. How is the maximum output determined?

The maximum output is determined by the production function, which shows the relationship between inputs and outputs. The point at which the marginal product of labor (the additional output gained by adding one more unit of labor) equals the marginal cost of labor (the additional cost of hiring one more unit of labor) is the maximum output level.

3. What factors can affect the maximum output and profit?

Several factors can affect the maximum output and profit, including the availability and cost of resources, technology, competition, and consumer demand. Changes in any of these factors can impact the production function and shift the maximum output and profit levels.

4. How do you calculate consumer surplus?

Consumer surplus is the difference between the price that consumers are willing to pay for a good or service and the actual price they pay. To calculate it, you need to know the demand curve, which shows the quantity of a good or service that consumers are willing to buy at different prices. The consumer surplus is the area below the demand curve and above the market price.

5. How can a company increase its consumer surplus?

A company can increase its consumer surplus by lowering the price of its products or services, as this will attract more customers and increase their willingness to pay. Additionally, improving the quality of the product or service can also increase consumer surplus, as customers will be willing to pay more for a better product. Understanding consumer preferences and offering discounts or promotions can also help increase consumer surplus.

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