Question

Exercise 6. Electric Cars vs. Gas Cars

You are buying a car that will cost you $500/mo in auto loan. Your gross monthly income is $4000, and net of your auto loan you have m=3500 at your disposal. Your x₁ is the miles you drive each month, and at the current gas prices your p₁=0.1 (ten cents in gas costs per miles driven). Your x₂ is consumption of everything else, with price normalized to p₂=1.

1. What is your budget line for a gas car? That is, x₂ = m/p₂ – (p₁/p₂)x₁.

2. You normally drive x₁ = 1000 miles a month. How much income do you have left for x₂?

3. You are considering getting an electric car instead. It costs more ($750/mo in auto loan), so that the income at your disposal would be m’=3250, but it costs less per mile driven: p₁’=.04 (electricity instead of gas). Write the budget line for the electric car. That is, x₂ = m’/p₂ – (p₁’/p₂)x₁.

4. Given your normal monthly miles consumption of x₁=1000, are you better off buying an electric car or a gas car? Show the difference.

5. You expect gas prices to go up. By how much should p₁ increase in order for you to change your mind?

6. The government is considering giving a monthly lump-sum subsidy, S, if you purchase an electric car. Given your monthly miles consumption of x₁=1000, how much should S be in order for you to change your mind?

Answer 1

We are supposed to do only four subpart to a question. For solution to other parts please post as separate question.

P = 0.1 = 1 Budget constraint: Pix + P₂ X ₂ = m. m=4000-500 m- 3500 put values of for P, and P2 and in 0.1 + ₂ = 3500 X 3500 -0.11 we get X = 1000 Income left for X = 3500 - Pixi X = 3500 -0.1 (1000) = 3400 x = $3400 Income left for Now P=0.04 and m= 3250 Budget Constraint: P x + P x2 = m 0.04x + x2 = 3250 x = 3250 -0.04x, x= 1000 y came xy = 3250 - 0.04 (100) X = 3210 I am worse this will lead other goods x off buying electric car because to fall in the consumption of from 3400 to 3210