Question

10.1 Utility Maximization Question Friday, Aprl 21, 3017 03 PM Each week, Jen likes to drink coffee and eat bagels in the morning either at work or at home on the weekends. Figure 1 lists the total utility that she receives at each quantity of cups of coffee and bagels, respectively. Additionally, Jen has a weekly budget of $12 to spend on consuming cups of coffee and bagels (and she always spends her whole coffee/bagel budget otherwise she gets grumpy!). The current prices she faces are $2 per cup of coffee and $1 per bagel. Use this information to answer the questions below. a) What is Jen's optimal consumption bundle? What is the total utility she receives from her optimal consumption bundle? Hint: use the Optimal Consumption Rule to solve this question. Figure 1: Jen's Coffee & Bagel Consumption ($12/Week) Bagels ($1/Bagel) Quantity Coffee (P $2/Cup) Quantity Total Utility (TU) Total Utility (TU) 0 0 0 0 1 10 1 2 19 2 14 27 3 18 4 34 21 40 23 5 5 6 45 6 24 49 7 24 8 52 8 23 54 21 10 55 10 18 11 55 14 11 12 54 12 8 The price of bagels has risen from $1 per bagel to $2 per bagel. Unfortunately, Jen's weekly budget for coffee and bagels r emains at $12/week. Figure 2 also indicates the total utility she receives at each quantity of cups of coffee and bagels has remained the same. Use this information to answer the questions below.

Answer 1

A. An optimal bundle is where Jane receives the highest total utility given her budget constraint. Her budget constraint is that she can only spend $12 a week on bagels and coffee. Jane will use her dollars in way that gives her highest utility per dollar. Now, from the given data, if Jane first buys a coffee, she gets 10 utility for 2 dollars, or 5 utility per dollar. If she buys a Bagel, she gets a utility of 8 for a dollar. So Jane will first buy a Bagel. Next, if she buys another Bagel for another dollar, she gets another 6 utility for a dollar, still higher than 5 per dollar utility from Coffee, so she will buy another bagel for a total utility of 14. Now if she buys another bagel, she will only get 4 utility. So now she will buy a coffee for 2 dollars and 10 utility. Her total utility till now is 24 and she has spent 4 dollars. We can keep calculating this way, taking the product which is giving us higher utility per dollar at the stage. This is shown in the below table for 12 dollars.

24/ Product Total Money spent Total utility Bagel Bagel Coffee 4 Coffee 33 Bagel 37 Coffee Coffee 52 Bagel 45 55

Shown above is her optimal bundle- with 4 bagles and 4 coffees and a total utility of 55.

B. Bagel's price has now increased to 2 per piece, effectively halving its utility per dollar. With this, the following is the optimal bundle, calculated the same way we calculated the one above.

19 Product Total Money spent Total utility Coffee 10 Coffee Bagel 6 Coffee Coffee Bagel 12 10

C. Her budget constraint- the income to spend on bagels and coffee is now $20. Rest remains same. For this the optimal utility bundle is given below.

Total Money spent Total utility 10 Product Coffee Coffee Bagel Coffee Coffee Bagel Coffee Coffee Bagel Coffee 10 12 14