An Employee of American Electricity PLC receives income partly in form of money salary of $W per month and partly in form of free electricity allowance (a fixed number of Kilowatts a month). If she wants, she can buy more electricity at the normal price P1 per kilowatts but for technical reasons she cannot resell the electricity. The value of her free electricity at the normal price is $V so her total remuneration package is worth $X= $(V+W).
1.Draw a budget constraint to reflect this monthly Salary package with money income on the vertical axis and electricity on the horizontal axis clearly identifying $X, $V and $ W.
2. On a separate diagram, reproduce the budget constraint and draw a selection of indifference curves that illustrate the situation where an increase in the price of electricity (from P1 to P2) causes the employee to reduce her electricity consumption.
3. Reproduce the first diagram and draw an indifference curve to illustrate the case in which the employee would be indifferent to her current remuneration package and a straight monetary salary of $Y where $Y < $X. You may assume here that the price of electricity is back at the normal level of P1.
The trick to answering number 1 is two recognize that a certain amount of the good is given freely. We show this in the budget constraint with a straight line. This means that the individual can have up to $V of electricity (for free) but they do not have the ability to substitute it for money income. You can see that the maximum for money income is $W, while the maximum for electricity is $V + $W/P1. This shows that money income can be used to purchase electricity, but it cannot go the other way. The variable $X is shown off of the axis, because it is the combination of $W and $V, and only occurs when $W is used for money (exclusively). If any amount of $W is used to buy electricity, we are no longer at $X.
Remember, this type of problem can also apply to things like food stamps, free housing, or other government program (possibly trust funds) where the choosing power of the agent in question is limited.