Budget Constraints
By Courtney Lillvis A budget constraint is a combination of goods a consumer can buy given the prices and his income. Budget Constraints force consumers to decide which goods are affordable, and this restricts what they can buy. This has nothing to do with bookkeeping or technical relationships, just planning. The equation for budget constraints is known as the budget set, and is expressed as:


Px and Py are the prices of goods X and Y
M is the amount of income a consumer has to spend.

If a consumer spends their entire income then the equation becomes:


A consumer can spend all their income but they can not spend more than their income.

This is the budget line.Manipulating this equation we can get a linear function of:
The slope of the line is Px/Py.

By taking this linear equation and putting it on a graph it will look like this:

Everything under the red line is an affordable combination.

So lets say you go to a store and you find a DVD you want and some beer. You only have $40. The movie you want is $20 and the beer you want is $15. So your budget set you look like this:
15+20 < 40
You would be under the red line, meaning you’re with in the budget line.
Now lets say you want better beer tonight, not the cheap stuff. The most you can spend is $40 so you only have $5 more to put towards beer.
Now lets say it was your birthday a few days ago and your Grandma sent you $30. That $30 added to the $40 you have gives you and income of $70 to spend. The price of beer and the price of the DVD stay the same. The line will move outward.

Now that you have $70 to spend you can buy more of both goods. You could buy two movie, each at $20 and beer at $15.
Or two packs of beer, each at $15 and one movie at $20.

Or you can buy two movies at $20 each and two packs of beer each at $15

Now lets say you get to the store and there is a sale on the movie you want. The movie now costs $18 and the beer stays at the price of $15. You have the original income of $60. The graph will now look like this:

Your new budget set will be:
15+18< 60

Because the change in price of the movie you can buy more beer.

There are two forms of budget constraints, soft and hard.
Soft budget constraints happen when the relationship between expenditures and earnings is relaxed because some of the expenditures will be paid by someone other than the company, or the person.
For firms there are
Soft Subsidies- these are granted by the government. This may occur when an area is trying to attract business.
Soft Taxation- this occurs when tax rates aren’t uniformed or the obligations aren’t enforced strictly. There can be soft taxation even if tax rates are high. This is another way to attract new businesses. Like in the Carolinas when they were trying to bring in new factories.
Soft Credit- the fulfillments of contracts aren’t enforced strictly, it assumes the debt won’t be repaid.
Soft Administrative Prices- Prices adjust to cost simultaneously or successively.
Examples of soft constraints:
The BMW plant that opened in South Carolina. In order for the state to get BMW to come there and not another state they offered tax breaks along with some other incentives. This would be soft taxation and soft subsidies.
Soft credit would be like when you borrow money from parents. When the money is lent out, it is under the pretense that it will be paid back, but later it isn't enforced.
Soft administrative prices are when prices are set by a bureaucratic institution.

Hard budget constrains happen when no matter how hard a person or company tries to cut losses they can’t. This can end in bankruptcy. Hard budget constraints emphasize punishment.
An example would be a person living beyond their means. Lately we have seen a lot of people filing bankruptcy because they didn't have fixed interest rates on their houses, or they used the balloon payments. No matter what cost these people cut out they are unable to make their payments because the housing market has changed along with interest rates.

Multiple Choice Questions

1) A budget set is expressed by the equation.
  1. (Q+PxX)(Q+PyY)= M
  2. PxX+M = PyY
  3. PxX+PyY ≤ M
  4. PxX+PyY ≥ M

The answer is c. PxX+PyY ≤ M.
  1. Is wrong because if you add the quantity to price you would not get the correct answer. Also you do not multiply good X and Y, you add them together.
  2. Is wrong because adding the price of good X added to M (income) can not equal the price of good Y. This would mean buying good X and Y would be more than income and you can not exceed income.
  3. Is correct.
  4. Is wrong because you can not spend more than your income. Good X plus good Y can be equal to M but can not exceed it.


Looking at this graph which circles are in the budget set? The bubget line is the red line.
  1. Purple, Blue, and Yellow
  2. Pink, Purple, and Yellow
  3. Blue and Green
  4. Blue, Green, and Yellow

The correct answer is b. Pink, Purple, and Yellow
  1. Is not correct because Blue is above the budget line, which means PxX+PyY > M
  2. Is correct because all three dots are under the budget line. All of these points would be <M
  3. Blue and Green are both above the budget line.
  4. The only point under the budget line.

3) If your income increases which way does the budget line move?
  1. Outward towards the north-east
  2. Downward towards the south-west
  3. Clockwise from the Y intercept
  4. Counter-clockwise from the Y intercept

The correct answer is a. outwards towards the north-east.
  1. Is correct because if you have more income you can buy more of both goods X and Y
  2. Is not correct because and increase in income would allow you to buy more of goods X and Y not less.
  3. Is not correct because you can buy more of both items, not more of just X
  4. Is not correct because you can buy more of both goods not less of X

4) If the price of good X decreases and the price of good Y stays the same the budget line moves how?
a. Outward towards the north-east
  1. Downward towards the south-west
  2. Clockwise from the Y intercept
  3. Counter-clockwise from the Y intercept

The correct answer is c.
  1. Is not correct because you can not buy more of both goods.
  2. This is what happens when you have less income, not a change in price.
  3. This is correct because the maximum amount you can buy of good Y does not change, but the maximum amount of good X increases.
  4. This is not correct because a shift counter-clockwise would mean the price of good x increased.

5) If you have an income of $50 which two items can you buy?
Shirt $20
Pants $40
Flip-Flops $15
  1. Shirt and Pants
  2. Shirt and Flip-Flops
  3. Pants and Flip-Flops

The correct answer is b.

  1. Is not correct because 20 + 40 > 50
  2. Is correct because 20 + 15 < M
  3. Is not correct because 40 + 15 > M

6) There are two forms of budget constraint. What are they?
  1. Large and small
  2. Light and Hard
  3. Soft and Rough
  4. Soft and Hard

The correct answer is d.
  1. Is not correct because it is Hard and Soft
  2. Is not correct because it is Hard and Soft
  3. Is not correct because it is Hard and Soft
  4. Is correct