Lecture 5

2023-04-01

MIT OCW 14.01SC L5 - Budget Constraints

MIT OCW 14.01SC - Lec 5 (Youtube)

  • Assuming for now (till 3rd lecture from the end) that income = budget. (No savings.)
    • Good enough assumption for typical Americans.
  • Assume income y given to us at the starting which we have to spend on pizza and movies.
  • y = Price_m * No of Movies + Price_p * No of Pizzas (y = Sum (P_i * X_i))
  • Straight Line on the Pizza - Movie Graph (Budget Line) Two budget lines
    • Slope of the line will be (-ve of price ratio) (-P_m/P_p)
    • This slope is called Marginal Rate of Transformation
  • Opportunity Cost
    • Oppertunity cost is the value of the forgone alternative.
    • E.g. A movie is costing us half a pizza. (In the example in the graph, BC_1)
  • Maximising Utility subject to Budget Constraint Indifference curves and budget line
    • Maximising Utility is equivalent to choosing furthest out indifference curve on the budget line.
    • Indifference curve will be tangent to the budget constraint!
    • The slope of the indifference curve = slope of the budget constraint!
    • Marginal rate of substitution = Marginal rate of transformation!
    • - (∂U/∂x_1) / (∂U/∂x_2) = - P_1 / P_2
    • This equation is basically saying (Marginal) Benefit = (Marginal) Costs (Of next pizza vs movie, etc.)
    • (∂U/∂x_1)/P_1 = (∂U/∂x_2)/P_2
    • Benefit of Next dollar on pizza expenditure = Benefit of Next dollar on movie expenditure
    • If that is not true, (let's say next dollar on pizza expenditure buys us more utility) then we can shift our optimum point towards pizza!
    • Corner solutions possible where the slopes will not be equal! Optimal point with 6 pizzas and 0 movies
  • Mental accounting
    • We solved the above case for only 2 things but in practice we may have more choices -> multidimensional graph
    • Or we can divide things into pairs!
    • Could divide budget into categories and solve for each category.
  • Govt policy:
    • If they wanted to lower pizza consumption (pizza causes obesity or whatever), they could tax pizza.
    • Higher price of pizza, flatter budget constraint line -> shifted optimal point, lower consumption of pizza.
    • They could also do something different, like change the way people think about pizza.
      • Think of pizza as entertainment, not food. -> Maybe people allocate less to entertainment -> Leads to lower consumption of pizza.
      • Called a Nudge in Behavioural Economics.