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!