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I'm currently working on a problem from Intermediate Microeconomics Workouts by Varian and I've become stuck on a particular question to do with monopolies.

We are given the demand curve for a monopolist:

$$ q = 160-2p $$

and the total daily costs:

$$C = 2000 + 10q$$

From this, I've found the profit-maximising price, quantity and daily profit which are as follows:

$$p* = 45$$ $$q* = 70$$ $$\pi* = 450 \text{ per day}$$

Now, the question I'm stuck on is: If the interest rate is 10% per year, how much will someone be willing to pay to own the monopoly?

My first approach was to simply multiply the total profits per day times 365 days times 1.1 to get the yearly profits with interest, but apparently that's incorrect.

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  • $\begingroup$ This is a very, very easy question if the profit is 450 per year. It's much harder if the profit is 450 per day, since you now need to discount day-by-day (e.g., convert that nice round 10% into something like the 365.25'th root of 1.1 and then calculate the perpetuity value from that.) $\endgroup$ – David Croson May 15 '17 at 2:26
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I'm not super clear about the policy here regarding self study questions. I'll give a hint for now.

You can translate the question into: finding the present value of a perpetuity, which is the present value of a constant and infinite sequence: (450*365, 450*365, ...)

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  • $\begingroup$ @Hessian that's when the interest rate comes in the PV calculation. $\endgroup$ – Paul Nov 3 '16 at 23:33

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