1. Doug consumes two goods, electricity, e, and a composite commodity z. Doug has the following utility function: U = z²-e Last week, he clicked on a Facebook ad and got free solar panels put on his roof! Now Doug has solar panels on his roof that generate 50 units of electricity per day. For the going price of electricity, if Doug demands more than 50 units of electricity, he can bu more at that price. If he demands less than 50 units, he can sell the extra electricity (5 - his consumption) back to the grid, and earn the going price as extra income. a. What are his Marshallian demand functions for e and z?
1. Doug consumes two goods, electricity, e, and a composite commodity z. Doug has the following utility function: U = z²-e Last week, he clicked on a Facebook ad and got free solar panels put on his roof! Now Doug has solar panels on his roof that generate 50 units of electricity per day. For the going price of electricity, if Doug demands more than 50 units of electricity, he can bu more at that price. If he demands less than 50 units, he can sell the extra electricity (5 - his consumption) back to the grid, and earn the going price as extra income. a. What are his Marshallian demand functions for e and z?
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.2P
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Transcribed Image Text:1. Doug consumes two goods, electricity, e, and a composite commodity z.
Doug has the following utility function: U = z²-e
Last week, he clicked on a Facebook ad and got free solar panels put on his roof! Now
Doug has solar panels on his roof that generate 50 units of electricity per day. For the
going price of electricity, if Doug demands more than 50 units of electricity, he can buy
more at that price. If he demands less than 50 units, he can sell the extra electricity (50
- his consumption) back to the grid, and earn the going price as extra income.
a.
What are his Marshallian demand functions for e and z?
b. Currently, Doug's income is $100 per day, the price of z is $1 and the price of
electricity is $0.50. How much electricity is he consuming and what is his utility? (note,
the utility numbers may get a bit large).
C
Calculate quantity demanded for electricity and his utility if the price of electricity
rises to $1. And then calculate the quantity demanded and utility when the price of
electricity rises to $2.
d.
Draw a graph to explain the phenomena that you see in your answers.
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