Exercise 7

Due Tuesday 10/29.

Part A

A recent graduate looking is looking for an apartment in the Washington area. She would like to have a spacious apartment but also plans to use enough heating and air-conditioning to be comfortable in winter and summer. She knows from experience that she will use exactly 1 kilowatt-hour (kWh) of electricity per square foot of floor space per month. Rents in the neighborhood where she would like to live are $0.90 per square foot per month, and electricity costs $0.10 per kWh.

1. Assuming she has $1000 a month to spend on rent and utilities, draw her budget constraint and a couple of her indifference curves. Show her equilibrium and calculate how many square feet of apartment space and kwh of electricity she consumes.
2. Now suppose she gets a promotion and can afford to spend $1500 on rent and utilities. Show her new equilibrium and calculate her consumption of each good.
3. Starting from the initial equilibrium in part (1), suppose the price of electricity rises to $0.20 per kWh. Calculate her new consumption bundle and show your results on a graph.
    
   

Part B

Parts B and C refer to the following survey data collected from several household about their consumption of goods X and Y over the last couple of years:

As you know, a household that regards two goods, X and Y, as perfect complements likes to have exactly b units (where b is a parameter) of the X good for each unit of Y. 

1. Please derive the household’s demand equations for X and Y in terms of b, Px, Py and income M.  Be sure to show the steps involved, don’t just write down the equations.
2. Next, use the demand equations and the information in the table to determine which of the surveyed households has perfect complements preferences and calculate the appropriate value of b.
3. Now suppose that in 2009, Px = $5, Py = $5 and the household identified in (2) has an income of $360.  Calculate the household’s consumption of each good.  Draw the budget constraint and include the numerical values of its intercepts.  Also sketch several of its indifference curves and show the household’s equilibrium on the diagram.  Be sure to show your work and label everything.
    
   

Part C

A household has preferences that can be represented by a Cobb-Douglas utility function. The function and the corresponding demand equations are shown below, where `g` is an unknown parameter and M is income:

1. Use the demand equations and the information in the table to determine which of the surveyed households has Cobb-Douglas preferences and calculate the value of g for that household.
2. Suppose that in 2009, Px = $5, Py = $5 and the household identified in (1) has an income of $300.  Calculate the household’s consumption of each good.  Draw the household’s budget constraint and include the numerical values of its intercepts.  Also sketch several of its indifference curves and show its equilibrium on the diagram.  Be sure to show your work and label everything.

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