Lecture 7 - Budget Constraints/Consumer Choice Flashcards
What is the format for writing a budget constraint?
Y = p1q1 + p2q2
- Y is the consumer’s income
- p1 and p2 are the respective prices of each unit of the two goods
- q1 and q2 are the quantities of goods 1 and 2 that are consumed
Can budget constraints be rewritten?
Yes, budget constraints can be rewritten to make any of the other variables the subject instead of Y
What are the two assumptions we make to write budget constraints?
1- Assume that individuals cannot save or borrow so that consumers have a fixed amount of money to spend now
2- Assume that consumers are price takers
What shape are budget constraints?
Budget constraints are straight lines which slope downwards
What is the gradient of a general budget constraint given by?
Gradient = -p1/p2
How can we calculate the Marginal rate of transformation?
The MRT is calculated by the gradient of the budget constraint
Define the marginal rate of transformation
The MRT is the marginal rate at which one good can be traded against the other in the market place
Write the general equation for a budget constraint in the form y=mx+c so it can be plotted on a graph
q2 = Y/p2 – p1/p2*q1
What does MRT measure?
MRT measures the opportunity costs of consuming one more unit of good 1 in terms of good 2
On an indifference map, interpret bundles above the budget constraint
On an indifference curve: Bundles above the budget constraint are not feasible
On an indifference map, interpret bundles below the budget constraint
On an indifference curve, bundles below the budget constraint are feasible but dominated by bundles on the constraint (non-satiation assumption)
On an indifference map, interpret bundles on indifference curves that cross the budget constraint
Bundles on indifference curves that cross the budget constraint are not optimal
On an indifference map, where is the optimal bundle?
The optimal bundle is on the highest indifference curve that just touches the budget line
‘Just touching’ means that the indifference curve is tangent to the budget constraint
When is a consumer’s utility maximised?
A consumer’s utility is maximised when MRS=MRT
How else can we write the utility maximisation condition?
1: MRS = MRT
2: -U1/U2 = -p1/p2
3: U1/p1 = U2/p2
How do we calculate the maximum utility a consumer can gain given their utility function and budget constraint?
1- Rearrange the budget constraint to make either q1 or q2 the subject
2- Substitute this into the utility function of the form U(q1,q2)
3- Rewrite the budget constraint all in terms of q1 or q2
4- Differentiate and make the derivative equal to zero
5- Solve for q1 or q2
6- Plug this back into the budget constraint to find the other value
7- Calculate the maximum utility using these two values
When finding the maximum utility for a utility function whose indifference curves doesn’t hit the axes, what type of solution is this called?
An interior solution
When finding the maximum utility of a utility function in which the two goods are perfect substitutes (indifference curves touch the axes), what type of solution is this called?
A corner solution
When does the utility maximisation rule of MRS=MRT not apply?
MRS=MRT does not apply when MRT>MRS
