Demand and Consumption Notes

Demand and Consumption

Two Categories of Consumption

When analyzing demand and consumption, it can be broken down into two main questions:

  1. How much do I consume in general?

  2. How do I divide that consumption amongst the things I like?

For example, imagine going to a restaurant with friends. First, one needs to decide how much money to allow oneself to spend. Then, once at the restaurant, decide what to order within that budget. Should one order seven Jagerbombs, or a poutine, or fish and chips with milk?

Modeling Consumption: The Budget

The next step is to figure out how to model how much someone can consume. This involves finding a way to model all the bundles of different goods that are affordable.

In the restaurant example, with $50, one could order two poutines, two burgers, one of each, or four drinks. It's a list of all affordable options within the budget. To create this list, one needs to know the price of the alternatives (goods or services) and how much money is available.

One isn't trying to figure out what one actually buys, but what one could buy. The preferences don't matter at this stage, only the budget and prices matter.

Information Needed to Model Affordable Bundles:

  • Prices of alternatives (goods/services)

  • Income (how much money is available)

Creating a Budget Equation

The next step is to create an equation that represents what's affordable. It will be simplified down to two alternatives to make the math easier and allow for graphing. This keeps the math manageable.

Even though people pick between more than two things, every choice can be framed as a binary choice between "this or that". For example, splitting money between food and drink, then deciding between beef, chicken, vegetarian, or poutine.

Important Rule:

There should be no money left over. Spending less would be inefficient. The decision of how much to save vs. spend should have already been made. This is a nested decision, with other decisions coming before it. For example, economists studying the labor market often model labor vs. leisure.

Mathematical Representation of a Budget

To construct the mathematical representation of the budget, here are the needed components:

  • mm: Money available (income, budget)

  • Price of the alternatives

For example, consider poutine and wheat tea (beer).

The initial incomplete equation:

m=Price of Poutine+Price of Wheat Team = \text{Price of Poutine} + \text{Price of Wheat Tea}

This equation is incomplete because it doesn't account for the quantity of each item purchased. It needs a variable to represent how much of each item is being bought:

  • ff: Quantity of fries purchased

  • Price of fries

  • Quantity of wheat tea purchased (l)

  • Price of wheat tea

The complete equation:

m=(Price of Fries×f)+(Price of Wheat Tea×l)m = (\text{Price of Fries} \times f) + (\text{Price of Wheat Tea} \times l)

The equal sign signifies that all available money will be spent on fries and wheat tea.

Optimization

This setup leads to an optimization problem: maximizing happiness based on the budget.

  • This can be solved with: Lagrange optimization

  • Or, it can be solved with economic logic

Graphing the Budget

The next step is to create a graph. The axes will represent the two alternatives (fries and wheat tea), unlike the supply and demand model where the axes are price and quantity.

The budget, mm, will be fixed because it will already be known how much money is available. For example, $50. Prices are also set within the model. As a consumer, one is given the price, and there's nothing one can do to change it. It's a fixed, exogenous number.

With fries on the x-axis and wheat tea on the y-axis, start by finding the two intercepts, because with two points in space, a line can be drawn connecting them.

The intercepts represent extreme scenarios: if all money is spent on fries, how many can be bought? If all money is spent on wheat tea, how many can be bought?

Example

  • Budget (mm): $50

  • Price of fries: $10

  • Price of wheat tea: $5

If spending all the budget on fries, one could afford 5. If spending all the budget on wheat tea, one could purchase 10.

Since the prices are fixed, the function is linear. As one decreases the amount of one item purchase, one always gets the same amount of the other item in return. Meaning the budget is just a straight line between the two.

Budget Line Analysis

Everything on the budget line costs exactly the full budget ($50 in the example). Consuming above the line is not affordable. Consuming below the line is an inefficient use of money. Therefore, optimal consumption will occur on the line.

Preferences

All this tells us is what is affordable, but not what the consumer will actually choose.

The difference in peoples choices is because of different preferences. To actually be able to model what someone chooses requires a mathematical measurement of preferences.

Manipulating the Budget

Changing m (Money Available)

Changing mm shifts the budget line. More money shifts the line outwards (away from the origin). Less money shifts the line inwards (towards the origin). The slope of the line does not change.

Changing the Price of Fries

If fries get cheaper, the budget rotates. The wheat tea axis intercept does not change, because the price of fries does not affect the price of wheat tea. The fries axis intercept moves outwards. If something gets cheaper, one can buy more of it.

One can get the same effect of moving the line outwards if both the price of fries and wheat teas were 50% off.

Slope of the Budget

The slope of the budget tells about the relative price of the alternatives. Price doesn't matter, relative price matters.

In the base case (fries = $10, wheat tea = $5), the slope is -2. This tells that fries are twice as expensive as wheat tea.

If fries go on sale for 50% off (fries = $5, wheat tea = $5), the slope is -1. The relative price of fries is now one wheat tea. They have the same relative cost.