Question

2.2 Electricity Pricing 1. Households in California pay approximately 15 cents per kilowatt-hour (kWh) for electricity. Assume a household is allocating their $300 monthly budget between electricity and a prepaid phone plan, which costs 30 cents per minute. What is this household's budget constraint? 2. Imagine there is a surcharge for high energy usage: the utility will charge 30 cents per kWh for all electricity consumption over 1000 kWh. Now what is the household's budget constraint? 3. What if this was a business that received a bulk discount of 10 cents per kWh over 1000 kWh? 2.23

Can someone explain the solution not really sure how they got the numbers for the graphs or what these budget constraints or equations look like in terms of numbers someone help step by step

Answer 1

1. see their income is $300

if they spend all of the money on electricity they can buy maximum 300/0.15=2000 units of electricity. given the price of electricity=15cents. hence the intercept of 2000 can be seen in the electricity axis. see at that point 2000 units of electricity is being consumed but no phone call is consumed.

if they spend all their money on phone call then they can buy no electricity and 300/0.30=1000 units of phone calls. hence the intercept of the phone call axis is 1000.

the budget constraint equation is, total income= price of electricity * units of electricity consumed+ price of phone calls*units of phone calls consumed

hence, 300=0.15xunits of electricty+0.30xunits of phone calls

the slope of the line is = -(price of the electricity/price of the phone call)= 0.5

put different values of units of electricity and solve for the phone calls you'll get the line shown in the diagram.

2. in the first example there were no over usage surcharge. now they are imposing an extra 30 cents on the electricity usage over 1000units. hence they can consume up to 1000units of electricity at price $0.15 but after 1000 units of electricity they have to pay $0.45.

hence if they spend everything on electricity, their maximum consumption will look like this

first they will consume 1000 units at $0.15x1000=$150

now over 1000units they have $150 left to consume electricity at $0.45. hence they can consume extra 150/0.45=333.33333 units of electricity.

hence their maximum electricity consumption= 1000+333.33333=1333.3333 units.

hence after the point where 1000 units have consumed the slope of the budget line will change and it will cut the electricity axis at 1333.3333 instead of 2000.

again from slope stand point the slope before 1000units of electricity= -(0.15/0.30)=-0.5

after the 1000units of electricity the slope becomes=-(0.45/0.30)=-1.5

hence the slope increases and it is evident in the diagram.

3. now in this question the price of the electricity falls to 0.05 after the usage of 1000units.

hence the after 1000 units of consumtption thety can buy 150/0.05=3000 units hence they can consume max 1000+3000=4000 units of electricty.

and the slope becomes after 1000 units=0.05/0.30=-0.1666

hence the slope falls as evident in the diagram.