marginal rate of substitution, budget constraint, specific question help

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Kim has an income of $100 a week and is observed consuming 5 sushi dinners at $15 per dinner and 10 ice cream sodas at $2.50 each. Through a series of questions we determine that her marginal rate of substitution for this consumption choice is 7.

  1. Explain why Kim isn’t maximizing her utility. To maximize utility should she increase (or decrease) her consumption of ice cream sodas? Sushi?[1] Illustrate your answer using a graph (put ice cream sodas on the X-axis and sushi on the Y-axis and assume that Kim has convex indifference curves).
  2. For this part of the question assume that Kim starts off at a combination of ice cream sodas and sushi that maximizes her utility given the prices and income level given above. Illustrate this starting point in a graph with indifference curves and budget constraints. Suppose the price of an ice cream soda increases to $4 each. Illustrate how Kim’s consumption changes in your graph. Show your answer by illustrating the substitution and income effects in your graph. Assume that ice cream sodas are a normal good. Explain.

[1] You can’t solve for the “exact” optimal solution. A general description of what she should do is fine.

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RUNNING HEADER: Utility Maximization

Utility Maximization 2

Given that Kim weekly income is M and prices, 𝑃𝑥 and𝑃𝑦, represent the price sushi dinner and
ice cream soda respectively. Kim problem is to select the affordable bundle that results to
maximizing her utility.
Her feasible set (budget): total expenditure should not exceed income, so we have
𝑃𝑥𝑋 + 𝑃𝑦𝑌 ≤ 𝑀……………………..1
Inequality (1) must hold with equality since more is better at the solution to the Kim problem.

𝑀 = $100
𝑃𝑥 = $15 And 𝑃𝑦 = $2.50
𝑋 = 5 And 𝑌 = 10

For a utility maximize condition 𝑃𝑥𝑋 + 𝑃𝑦𝑌 =...

anaplJ (2991)
University of Virginia

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