Question

3. The monopolist faces a demand curve given by D(p) = 10p-3 . Its cost function is c(y) = 2y. What is its optimal level of output and price?

Answer 1

using diffrerential calculus

Answer 2

-> R (y) = (10y -3) 2y
= 20y² - 6y
-> R' (y) = 40y - 6
Optimal level of output when R' (y) = C'(y)
-> 40y - 6 = 2
=> 40y = 8
=> y = 8/40 = .2

Answer 3

thanks but why did u substitute the p for y ? additionally i need to solve for p-price

Answer 4

The reason why it takes so long because the question doesn't explain which one is quantity!

Answer 5

oh my there is a correction also, the fuction is actually \[D(p)=10p ^{-3}\]

Answer 6

The concept is find Revenue: quantity * unit price
R (y ) = (10/ y³ ) * 2y = 20/ y²
In order to gain optimal output:
R' (x) = C'(x) --> - 20/ y = 2 => y = -10
Plug it back to get unit price!

Answer 7

There's so much confused in the way the asker posting! I just show you the concept with sample, then you can figure out for next problems.

Answer 8

thanks now i follow

Answer 9

i think. still reading though, but kinda make sense

Answer 10

optimal output = maximizie profit
=> marginal revenue = marginal cost!

Answer 11

yea i know

Answer 12

It's weird that the result negative ???

Answer 13

What course is it? Do you have the examples to practice with?

Answer 14

it Intermediate microeconomics II , by problem is the demand curve funtion, usually they give function int terps of quantity eg P=700 - 5Q but now the funtion is in terms of price so i was a bit confused, proably still am

Answer 15

I'm reading the material, hopefully I'll be able to clarify it for you!

Answer 16

thanks alot

Answer 17

This is online example, both Price and Cost depends on quantity Q:
P = 100 − Q ( price function from demand)
C(Q) = 20 Q ( Cost function)
Find the monopolist quantity (Qm), price (Pm):
MR = MC
100 − 2Q = 20
=⇒ Qm = 40 units ,
Pm = 100 - 40 = $60

Answer 18

i'm wondering where they got marginal revenue = 100 - 2Q

Answer 19

I'm glad that I don't take this course, good luck!

Answer 20

thanks, wish i didnt either :( lol

Answer 21

im wondering if they took the q from the other side leaving the 20 and gettin 2q

Answer 22

I feel so bad that I can't be more helful :(
http://ebooks.narotama.ac.id/files/Intermediate%20Microeconomics;%20A%20Modern%20Approach%20%288th%20Edition%29/Chapter%2024%20Monopoly.pdf

Answer 23

Hopefully you can find some useful from the link!