Question

In order to submit this assignment, you will use this webform to upload a document file (.doc) or (.docx) with your answers. You may use a drawing program or sketch by hand. Be sure that your responses model clear economic reasoning and addresses each of the following:

1.) For this exercise you will need to first build a graph to these specifications: Draw a budget constraint with vertical intercept (0,8) and horizontal intercept (4,0). Zach’s indifference curves are downward sloping straight lines with a slope of -1 i.e. they all have vertical intercept (0,N) and horizontal intercept (N,0) for some number N. Draw Zach’s indifference curves. Label the bundle(s) that Zach will consume when optimizing.

2.) Now suppose the price of the “x-good” falls to become 4 times smaller than it was originally. Draw Zach’s new budget constraint. Draw in Zach’s indifference curves and label the new optimal bundle(s). Interpret Zach’s indifference curves: are the good substitutes or complements to Zach?

3.) Emily likes pretzels and Pepsi. She bought 12 bottles of Pepsi for $3 each. Her marginal utility for the twelfth bottle was 9 utils. She also bought 5 bags of pretzels for $4 per bag. Her marginal utility for the fifth bag was 8 utils. Assume Emily exhausted her budget on this purchase of Pepsi and pretzels, but wanted to maximize her utility. Would she have been better off buying more Pepsi and fewer pretzels, more pretzels and less Pepsi, or was her purchase already optimal? Assuming her marginal utilities are constant across all levels of consumption. Are pretzels and Pepsi complements or substitutes to Emily?

Answer 1

1)

The indifference curve are given by the red straight line with slope -1. The further the curves are from origin the higher is the uility.

2)

As the price of X falls, budget line shifts from Ab to AC. As a result consumption of X increases. X and Y substitute good. So as now X is cheap people buy more X than Y.

Px*X+Py*Y=M. Slope decrease as the price of X falls. So budget line becomes flatter.

3)

Utility is maximized when

MU(Pretzel) / Price of Pretzel = MU(Pepsi) / Price of Pepsi

Here,

MU(Pretzel) / Price of Pretzel = 5/4 = 1.25

MU(Pepsi) / Price of Pepsi = 12/3 = 4

Since [MU(Pretzel) / Price of Pretzel] < [MU(Pepsi) / Price of Pepsi], utility is not maximized. She should buy more Pretzel and less Pepsi.

Since Emily buys both the goods together, Pretzel and Pepsi are complements in consumption for her.