# A monopoly firm faces a demand curve given by the following equation: P = \$500 − 10Q, where Q equals quantity sold per day. Its marginal cost curve is MC = \$100 per day. Assume that the firm faces no fixed cost. You may wish to arrive at the answers mathematically, or by using a graph (the graph is not required to be presented), either way, please provide a brief description of how you arrived at your results.

a) How much will the firm produce?
b) How much will it charge?
c) Can you determine its profit per day? (Hint: you can; state how much it is.)
d) Suppose a tax of \$1,000 per day is imposed on the firm. How will this affect its price?
e) How would the \$1,000 per day tax its output per day?
f) How would the \$1,000 per day tax affect its profit per day?
g) Now suppose a tax of \$100 per unit is imposed. How will this affect the firm’s price?
h) How would a \$100 per unit tax affect the firm’s profit maximizing output per day?
i) How would the \$100 per unit tax affect the firms profit per day?

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1. Use the demand curve to derive MR.
NOTE: MR is always two times steeper than the demand curve if the equation is linear.

Hence, MR=\$500-20Q.

Use MC=MR

100=500-20Q
20Q=400
Q=20

P=500-10(20)=400.

Profit per day= There's no AC so I can't locate it.

In terms of tax. If it is a lump sum tax and proportional tax it won't affect the current profit maximizing price and qty.

However, tax per unit will affect profit maximizing.

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2. @Samuel
"There's no AC so I can't locate it."
=> Since the marginal cost is stable (although that is very unlikely to happen in the real world it is the case here) and there is no fixed cost, the AC is 100.

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