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the demand for personal computers has been estimated to be Q = 500,000

          the demand for personal computers has been estimated to be Q = 500,000
        

Added by Gail B.

Principles of Economics
Principles of Economics
Gregory Mankiw 8th Edition
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the demand for personal computers has been estimated to be Q = 500,000
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The demand for personal computers in the home goes up with household income. For a given community, we can approximate the average number of computers in a home as $$q=0.3454 \ln x-3.047 \quad 10,000 \leq x \leq 125,000$$ where $x$ is mean household income. ${ }^{60}$ Your community has a mean income of $\$ 30,000$, increasing at a rate of $\$ 2,000$ per year. How many computers per household are there, and how fast is the number of computers in a home increasing? (Round your answer to four decimal places.)

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Transcript

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0:00 Hello.
00:01 To determine the size of the shortage, we need to calculate the quantity demanded and the quantity supplied at the price of $6 ,000 using the demand and supply equations provided.
00:09 So here's a step -by -step calculation.
00:11 So first, we're looking at the quantity demand.
00:13 We have the equation set as p equals 30 ,000 minus 2q.
00:20 To find the quantity demanded at a price of $6 ,000, we substitute p with $6 ,000.
00:25 So we have $6 ,000 equals $30 ,000 minus 2q.
00:31 And we can rearrange and simplify this equation where we get 2q is equal to $24 ,000.
00:40 And then divide by 2 on each side, and you're going to get that q is equal to $12 ,000.
00:46 So the quantity demanded at $6 ,000 is 12 ,000 computers.
00:51 Excuse me, computers.
00:56 Now we can look at the quantity supplied, and it's a pretty similar equation...
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