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Econs, Quantitative Analysis HELP PLS!

I've been given only the demand and selling price

Demand (000's)
4
6
9
11
13
14
16
18.5

Selling price
38
36
32
23.5
24.5
20
14.5
12.5

The unit variable cost: 15
Fixed Cost: 20,000

I've found the consumer demand function through correlation and regression, that is p= 46.72 - 1.89q. I've also plotted a scattergraph.

The second question says to find the selling price and output for the company to maximise short-run profits. How would I go about finding the MR with the equation? and plotting the MC and MR. An explanation would be greatly appreciated. Thank you.
basically, multiply q with p to get the revenue. This will give you 46.72q - 1.89q^2

now take away (15q + 20000) as this is the cost

differentiate what is left, i.e. 46.72q - 1.89q^2-(15q + 20000) to find the apex of the parabola

you should get the answer.
Reply 2
Avatar for amethystfrenzy
amethystfrenzy
OP
I did that, thank you thank you. So meaning to say the revenue function is: 46.72q - 1.89^2

Then minus by total cost which is 15q +20000. that would give me the profit right?

Once that's all done, I have to put it into the quadratic formula? What about finding the extra cost of producing one extra unit as I've to plot MC and MR on the graph.
Original post by amethystfrenzy
I did that, thank you thank you. So meaning to say the revenue function is: 46.72q - 1.89^2

Then minus by total cost which is 15q +20000. that would give me the profit right?

Once that's all done, I have to put it into the quadratic formula? What about finding the extra cost of producing one extra unit as I've to plot MC and MR on the graph.


Well yes that would give you the profit. But then you have to differentiate what the profit is. You'll get -3.78q + 31.72. Equate this with 0 and solve for q to find the quantity at which profit is maximised.

As for marginal cost, i presume that would be a straight line with gradient 15, since that is the unit variable cost. Marginal revenue should be the rate of change of revenue, so differentiate the revenue function and plot that on your graph.

I'm only an AS student so im sorry if i can't solve your problem any further:redface:
Reply 4
Avatar for zedeneye1
zedeneye1
18
Original post by The Wayfarer
Well yes that would give you the profit. But then you have to differentiate what the profit is. You'll get -3.78q + 31.72. Equate this with 0 and solve for q to find the quantity at which profit is maximised.

As for marginal cost, i presume that would be a straight line with gradient 15, since that is the unit variable cost. Marginal revenue should be the rate of change of revenue, so differentiate the revenue function and plot that on your graph.

I'm only an AS student so im sorry if i can't solve your problem any further:redface:


how come u know sooooo much at just AS level?? wat other subs do u have?
Reply 5
Avatar for amethystfrenzy
amethystfrenzy
OP
Thank you SO much. Omg for an AS level student, you sure know alot. This is degree level!! Calculations are my least fav sub hence the struggle. What other subjects do you do?

Greatly appreciated. thank you again for having me on the right track..from there I can finally work it out.
(edited 12 years ago)

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