# economic math

Imagine that you own a small business and that you have to decide how much of your product to sell every year, and which technology to use to produce it.

Your market research suggests that the price at which you will be able to sell each unit of your product is given by 200−q, where q denotes the total amount sold over the course of the year.

You have access to two different technologies, which you can use in any feasible combination. The technologies have different cost properties. Producing q units with the first technology costs 100q. Producing q units with the second technology costs q2.

QUESTION. How many units should be produced using the first technology at the profit maximizing decision?

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1. what i am getting is q equal to 50 but i know its wrong...so even i m waiting for the right answer!

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posted by surbhi
2. can not get it to work at all.... 4 guesses left.. I can tell you its not 1 2 50 100

3. pretty easy my friend. i do in my sleep this question. think of shape of 'marginal' cost. It take two characteristics, first characteristic linear increase in price from "second technology alone" to point q=50, then constant value of 100 from "first technology alone". Why? Because we want keep cost down my friend. So marginal cost (MC) = 2q when q<= 50; and marginal cost = 100 for q > 50. Now we look at marginal revenue (MR). MR = derivative of (200-q)*q = 200 - 2q. Now plot on graph and with boundary constraints you need obtain solution closest to intersection point of both shapes. obvious point this is q=50. So all production make by technology 2 and nothing technology 1. I go sleep my friend, after drink little bit vodka. cheers from russia

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posted by sputnik
4. Many thanks my friend!!!

5. used graphing calc. clear as day

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6. the right value is zero

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posted by manu
7. Your market research suggests that the price at which you will be able to sell each unit of your product is given by 200−q, where q denotes the total amount sold over the course of the year.

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