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# Widget Corp: Regulation of a monopoly. Detailed calculations

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The widget industry in Anytown is a monopoly, controlled by Widget Corp. Its demand curve for the local market is given by
P = 800 - 20 W
Where W represents the number of widgets sold per period.
The total cost function (including opportunity or implicit costs) for Widget Corp. is
TC = 300 + 500 W + 10W^2

a. Assuming the industry is unregulated, what are the equilibrium price and output and economic profits earned by Widget Corp.?
b. If the industry is regulated and the regulatory authority forces Widget Corp. to earn only a normal return on investment (which is included in its cost function), what is the resulting equilibrium price and quantity?
c. What happens to consumer surplus? What happens to the economic profits earned by Widget Corp.?

##### Solution Summary

The widget industry in Anytown is a monopoly, controlled by Widget Corp. This solution gives detailed calculations to determine Widget Corp's price and output, as well as its total cost, total revenue and profit.
When the industry is regulated, the regulatory authority forces Widget Corp. to earn only a normal return on investment. The solution gives detailed calculations showing the effect on equilibrium price and quantity, as well as the consumer surplus and Widget Corp's economic profit.

##### Solution Preview

a) When the industry is unregulated, Widget Corp maximizes its profits by selling the number of widgets at which its Marginal Revenue (MR) equals its Marginal Cost (MC).

To find MR, first find Total Revenue (TR). TR is Price times the number of Widgets sold, so:
TR = PW
TR = (800 - 20W)W
TR = 800W - 20W^2

MR is the derivative of TR:
MR = 800 - 40W

MC is the derivative of TC:
TC = 300 + 500W + 10W^2
MC = 500 + 20W

Set MR equal to MC to find out how many widgets WidgetCorp will sell.
800 - 40W = 500 + 20W

Solving this equation will tell you the equilibrium output (W), which you can use to ...

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