df ( x)
(4e ( x 4 x ) ) (4 x)(2 x 4)e ( x 4 x )
2 2
dx
2-
The total cost function for a manufacturer has the following form,
TC= 2Q3 - 45Q2 + 300Q where Q is the output level.
a)Find the level of output, which minimises the total cost,
b)Find the average cost at the production level, which minimises the cost.
a) FOC: MC 6Q 2 90Q 300 0 Q=10 , Q=5
SOC: MC ' 12Q 90
Q=10 MC’=30>0 Minimum, therefore Q=10 minimises the Total cost
Q=5 MC’=-30<0 Maximum
b) Q=10 TC = 500 AC=50
3-
The total revenue and marginal cost functions of a manufacturing firm have been defined as
TR = 5900Q-10Q2 MC = 6Q2 -8Q +140
where Q is the output level. If the firms fixed cost is 845, Find:
a)The level of output, which maximises the total revenue,
b)The maximum revenue
c)The level of output, which maximises the firm’s profit,
d)The total cost when profit is maximised,
e)The average cost when profit is maximised.
a) FOC: MR = 5900 – 20Q = 0 Q=295
SOC: MR’ = -20 <0 therefore Q=295 is the level which maximises TR
d 2 d 2
SOC: 12Q 12 Q=30 372 0
dQ 2 dQ 2
Q=30 maximises profit
d) We need to find the total cost when profit is maximised, but we know only MC and not TC i.e. we
know that
TC MC TC 6Q 2 8Q 140
We need to find the function that if we differentiate it will give us TC.
However basic differentiation rules state that: Q 1 , Q 2 2Q and, Q 3Q
3 2
The final total cost function includes also a fixed cost of 845, So:
TC 2Q3 4Q 2 140Q 845
And, for Q =30:
TC(30) = 55,445
e) AC = TC/Q = 55,445/30=1,848.167
4-
Given the following demand function,
Q=100-24P
a)Find the price elasticity of demand at P=1 and P=3,
b)Find the price at which the price elasticity demand is unity,
c)What is the relationship between the price level in part (b) and the supplier’s revenue?
a)
P=1 Q=76 , P=3 Q=28
121
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller grade_bender. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £11.06. You're not tied to anything after your purchase.
