Exercise 1
Subject:EconomicsPrice: Bought3
Exercise 1.3: Solve for the optimal consumption bundle using a budget constraint and an indifference curve. For the budget constraint, the consumer has $3,000 to spend, and wishes to spend their money on good X, at a price of $10 per unit, and the composite good, at a normalized price of $1 per unit. For the indifference curve, the MRS measured at any point along that indifference curve can be found by the formula 2X I = $3000; P = $10; P, = $1 The optimal consumption bundle occurs where the furthest out obtainable indifference PX curve has a point of tangency with the budget constraint. I.e. where the MRS = Py Y 10 Therefore: Y = 20% (equation 1) 2x And: I = P_X +PJY - 3000 = 10x + y (equation 2) Substituting equation 1 into equation 2: 3000 = 10X + Y - 3000 = 10x + 20X - 3000 = 30X → X = 100 units. Substituting this value of X into equation 1 to get Y: Y = 20 * 100 → Y = 2000 units. The optimal consumption bundle contains 100 units of X and 2000 units of Y.
