Choice

Question 1

What is Rational Constrained Choice?

Answer 1

• Decision-maker chooses their preferred alternative from available resources
• Available choices constitute choice sets

Question 2

Where is the optimal consumption point? What does it mean?

Answer 2

• Point α shows the highest utility given the budget constraint line
• This means that the point is where the constraint meets the indifference curve
• Denoted by x *1 (p1,p2,m) and x *2 (p1,p2,m), where if both x *1 and x *2 is >0 the solution is INTERIOR

Question 3

What conditions do x *1 and x *2 satisfy?

Answer 3

• The budget is exhausted,
  p1x *1+ p2x *2 = m
• The slope of the MRS = slope of the budget,
  MRS (x *1, x *2) = -p1/p2

Question 4

How can you compute Ordinary demand (mathematical operations)?

Answer 4

• Cobb-Douglas
• Optimisation via Lagrangian

Question 5

Using the Cobb-Douglas method, what does x *1 and x *2 equal?

Answer 5

• x*1 = a / a+b * m/p1
• x*2 = b / a+b * m/p2

Question 6

What is the Lagrangian function? Explain what λ is and how will x* 1 and x* 2 be calculated

Answer 6

• L = U(x1,x2) - λ(p1x1 + p2x2 - m)
• λ is the shadow price and illustrates what the change in u stems from a change in m
• Differentiate L w.r.t x1, x2 and λ
• Solve in terms of p1, p2 and m and rearrange for x* 1 and x* 2

Question 7

Give some special examples of x* 1 and x* 2 in certain situations (CHOICE)

Answer 7

• Perfect Substitutes: If p1>p2, you shouldn’t purchase any of x1 as x1~x2
• POINT (M/p1, 0) if P1<P2 OR (0,M/p2) if P1>P2
• Perfect Complements: The solution is at the corner of L
• Calculated by substituting ax1 = x2 into p1x* 1 + p2x* 2 = m
• POINT = (M / [p1 + ap2], aM / [p1 + ap2])