L8 - Constrained Optimisation Flashcards
What is a buyer’s choice constrained on?
What they can afford.
This depends on:
Income
Price of Goods
What is a price taker?
Price is constant regardless of how much they buy.
- Expenditure cannot be greater than income
How do you calculate total expenditure?
Price X How much you bought
-Typically denoted as 2X or 5Y etc.
Where 2 is price and Y is how much bought
What is a Budget Constraint?
-Shows which bundles are just affordable given income
- Feasible set consists of all affordable bundles
-Where the slope shows the trade-off
(SEE DIAGRAM IN NOTES)
What happens to the budget constraint when there’s an increase in income?
- Budget constraint shifts to the right as income rises
- Slope of the budget constraint remains the same
What happens to the budget constraint when there’s an increase in price?
- The budget constraint pivots as prices goes up
- Intercept remains constant,
(DIAGRAM IN NOTES)
What happens to the budget constraint when there’s a quantity discount?
Budget constraint only linear if price per unit same for all units. So it becomes non-linear.
Price is lower when goods are bought in bulk
(DIAGRAM IN NOTES)
What happens to the budget constraints when there’s a rationing of quantity?
- Sometimes governments ration how much can be bought when goods are scarce.
- In this case, the feasible set is not only determined by affordability.
-Along the vertical part of the budget
constraint, the slope is infinite. Equivalent
to price of infinity for another unit!
(DIAGRAM IN NOTES)
How do you find what the individual will actually choose (THE INTERIOR SOLUTION)?
Combining an indifference curve (Showing preferences) and Budget Constraint (Showing feasible choices).
Optimal choice is point where budget constraint tangent to Indifference Curve. At this point the slope equals slope of indifference curve.
(SEE DIAGRAM ON NOTES)
What does the slope of an indifference curve show?
This shows the rate at which an individual will trade one good for another
To see this, consider an individual’s willingness to exchange
The negative of the slope is the MRSyx (Marginal Rate of Substitution). Diminishing MRS for well behaved preferences (bundle of goods)
MRSyx = Px/Py
What are the properties of the Interior Solution?
At the optimal choice, the slope of the budget constraint is the same as the slope
of the indifference curve
What’s the Corner Solution?
- Situation in which consumers don’t buy certain products and rationing.
- Optimal choice is a ‘corner solution’
