L8 - Constraint Optimisation

Question 1

How do you set up a Budget constraint?

Answer 1

• like in D1

Income ⩾ Total expenditure
Income ⩾ P{1}x + P{2}y

Question 2

What does a budget constraint show?

Answer 2

• The budget constraint shows which bundles are just affordable given income
  The feasible set consists of all affordable bundles

Question 3

How is the Budget constraint effected by a increase in income?

Answer 3

• The budget constraint shifts to the right as income rises

- The slope of the budget constraint remains constant when income changes

Question 4

How is the Budget constraint effected by a increase in price?

Answer 4

• The intercept remains constant of the product whose price hasnt changed
• the budget constraint then pivots as the price goes up

Question 5

What does the slope of the budget constraint show?

Answer 5

Slope shows rate at which an individual can trade one good for another

Question 6

How is quantity discounts a non-linear budget constraint?

Answer 6

• The budget constraint is only linear if the price per unit is the same for all units
  Sometimes the price is lower when goods are bought in bulk
• therefore at a certain quantity of a product, the line then pivots from that point

Question 7

How is quantity rationing a non-linear budget constraint?

Answer 7

• Sometimes governments ration how much can be bought when goods are scarce
• In this case, the feasible set is not only determined by affordability
• at the set rationed quantity the budget constraint become vertical/horizontal
• along this part the slope is infinite. Equivalent to price of infinity for another unit!

Question 8

What is the Interior Solution?

Answer 8

• Indifference curves show preferences. Budget constraint shows feasible choices
• Putting them together shows what the individual will actually choose –> this is the interior solution
  -The optimal choice is at the point where the budget constraint is tangent to the
  indifference curve
• At this point the slope of the budget constraint equals the slope of the indifference curve

Question 9

How can the slope of a indifference curve be interpreted?

Answer 9

• his shows the rate at which an individual will trade one good for another
  To see this, consider an individual’s willingness to exchange
• The slope shows the worst acceptable terms of trade for an individual to substitute one for another
• At a particular point, the negative of the slope is
  called the marginal rate of substitution: MRS{yx}
• There is diminishing MRS{yx} for well-behaved preferences

Question 10

What are the properties of the Interior Solution?

Answer 10

• At the optimal choice, the slope of the budget constraint is the same as the slope of the indifference curve
• MRS{yx} shows rate at which an individual is willing to trade one good for another
• MRS{yx} = p{x}/p{y}
• p{x}/p{y} shows rate at which an individual can trade one good for another
• this is the opportunity cost of unit x in terms of unit y
• which is the amount of unit y that must be given up to obtain another unit of x depends on this ratio

Question 11

What is the corner solution?

Answer 11

• this can occur due rationing
• In these cases, the optimal choice is a “corner solution”
• so either they are only willing to have on type of product and are unwilling to trade it for the other
• OR the individual is willing to trade one product for another but due the quantity constraints this occurs at the ‘corner’ of the budget constraint