Question content area

Part $1$

There are

$1010$

households in Lake$$Wobegon$,$ Minnesota, each with a demand for electricity of

Upper Q equals $50$ minus Upper PQ$=50$P$.$

Lake Wobegon$$Electric$\text{'}$s $($LWE$)$ cost of producing electricity is

TC equals $500$ plus Upper QTC$=500+$Q$.$

Part $2$

a$.$ If the regulators of$$LWE$,$ in the short$$run$,$ want the lowest possible price for consumers in this$$market$,$ what price will they force LWE to$$charge$?$ What will output be in that$$case$?$ Calculate consumer surplus and$$LWE$\text{'}$s profit with that price. $($Round all responses to two decimal$$places$.)$

The regulated price would be

$$$$11,$

and the firm would produce

$490490$

units of electricity.

Total consumer surplus would be

$$$$1200512005,$

and the firm would earn a

$$$negative $500500$

profit.

Part $3$

b$.$ If regulators want to ensure that LWE$$doesn$\text{'}$t lose$$money$,$ what is the lowest price they can$$impose$?$ Calculate$$output$,$ consumer$$surplus$,$ and profit. Is there any deadweight$$loss$?($Round all responses to two decimal$$places$.)$

The regulated price would be

$$$$2\mathrm{.}042\mathrm{.}04,$

and the firm would produce

$479\mathrm{.}57479\mathrm{.}57$

units of electricity.

Total consumer surplus would be

$$$$1150011500,$

and the firm would earn a

$$$$00$

profit.

$$Finally$,$ there will be a deadweight loss of

$$$$5\mathrm{.}405\mathrm{.}40.$

Part $4$

c$.$ Kristina knows that deadweight loss is something that this small town can do without. She suggests that each household be required to pay a fixed amount just to receive any electricity at$$all$,$ and then a$$per$-$unit charge for electricity. Then LWE can break even while charging the price calculated in part$($a$).$ What fixed amount would each household have to pay for$$Kristina$\text{'}$s plan to$$work$?$ Why can you be sure that no household will choose instead to refuse the payment and go without$$electricity$?($Round your response to two decimal$$places$.)$

If each household pays a fee of

$$$enter your response here

and LWE charges the price calculated in part$($a$),$ there will be no deadweight loss and the firm will breakeven.$$Moreover$,$ households will pay the fee because it is

$$

$$

less than

greater than

equal to

the consumer surplus per household.