# Deriving Single Good Demand Curve

came across a problem set that I had no clue how to tackle, but looks painfully simple.

It's a market for electricity where households utility is represented by:

U(E) = aE - 2mL2 (Household Utility) C(E) = wE + FC (Firm cost function)

Where E is quantity of Electricity and L is daylight available at the households, and FC is a fixed cost, with a,m,and w being constant variables. The problem required deriving the Demand and Supply Curves and then getting the Competitive Equilibrium values for price and quantity as a function of the variables.

Typically, with a two good market, I would derive the marginal utility and equate them over their prices to obtain a value for one good and substitute that into the income constraint to get the demand as a function of one good. However, I can't work this out at all! Daylight doesn't have a price and I'm at a loss for how to derive demand. Similarly with Supply, if I take MC = w, would the supply curve simply be w?

Thanks for all of your help!

• Daylight doesn't have a price in this example, nor should you need it to solve the problem. The firm always has the same marginal cost, yes, so as long as the price of electricity is above $w$, it should produce as much as the consumer is willing to buy. The customer's marginal benefit from electricity is always the same, no matter how much sunlight there, so what do these things tell you? Sep 15 '18 at 23:04
• It is also worth mentioning the question would benefit from making it clear as to whether this market were perfectly competitive or a monopolist's market. Sep 15 '18 at 23:05