Budget constraints and consumer choice

Question 1

What are the two assumptions in budget constraints

Answer 1

• Assume that all income must be spent
• Assume that consumers are price takers

Question 2

What is marginal rate of transformation (MRT)

Answer 2

• the rate at which one good can be traded for another within the marketplace
• the opportunity cost of consuming one good compared to another in terms of income

Question 3

When is the consumer’s utility maximised in terms of budget

Answer 3

When MRS=MRT

Question 4

How can you rewrite MRS=MRT

Answer 4

Can rewrite the MRS = MRT condition as follows:
𝑀𝑅𝑆=𝑀𝑅𝑇↔−𝑈1/𝑈2 =−𝑝1/𝑝2 ↔ 𝑈1/𝑝1 =𝑈2/𝑝2
Intuition: The amount of extra utility from pizza per pound spent on pizza must equal the extra utility from burritos per pound spent on burritos.
If U1/𝑝1 > 𝑈2/𝑝2, could increase utility by consuming more pizzas and fewer burritos.
If 𝑈1/𝑝1 < 𝑈2/𝑝2, could increase utility by consuming fewer pizzas and more burritos.

Question 5

How can you represent consumer’s choice mathematically

Answer 5

The consumer wants to maximise their utility subject to (s.t.) their budget constraint

maxU (q1,q2)
s.t. Y = p1q1 + p2q2

Question 6

How to find the interior solution from consumers choice

Answer 6

1. Solve the budget constraint for q1 or q2

Y= p1q1 +p2q2
q1=(Y-p2q2)/p1

2. Substitute into the utility function
   maxU [(Y-p2q2)/p1,q2]
3. Differentiate with respect to q2
4. Use the rewritten budget constraint from step 1 to solve for q1