Econ 172

Fall  2007

 

HW 3  Due Wednesday September 19

 

 

Chapter 4

Questions:

2, 4,  7 (assume that initially, there is no sales tax, and then the sales tax is implemented), 10, 16, 18, 

2.  Gasoline purchased in the US and in Canada are perfect substitutes; hence indifference curves are straight lines with a slope (MRS) of -1.  If gasoline used to cost less in the US, then the consumer would buy all her gas in the US, at the Y intercept of the budget line.  When US taxes rise and gas is more expensive in the US, she will buy all her gas in Canada, at the X axis intercept.. 

 

 

 

 

 

 

 

 

 

 

 

4. Assume the neutral good is on the Y axis.   Indifference curves are then parallel vertical lines

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7.(Assume that initially, there is no sales tax, and then the sales tax is implemented.)

Initially the budget line and indifference curve has the standard tangency along I2.  When the sales tax on clothing is implemented, the budget line moves inward along the clothing axis.  The new equilibrium is on I1, with less clothing consumed.  Spenser is now worse off.

 

 

 

 

 

 

 

 

 

10.  The poor person has and income of $1,000 and receives $100 of food stamps.  The person can sell the stamps on the black market for less than their face value.  The new budget line intersects the food budget line 100 units to the right of the old x axis intercept (assume food costs $1 per unit).

At anything less than 100 units of food, the budget line has a kink.  If $100 worth of food stamps can be sold for $50, then the composite good (money income) intercept is $1050.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

16.  Julia consumes anchovies A and biscuits B.  When A=2 and B=2, her MRS is given at  -1 = MUa/MUb.

Would she prefer a bundle with 3 cans of anchovies and 1 box of biscuits to a bundle with two of each?  At this initial point, her MRS is -1.  That means her marginal utility for the 2 are equal (since MUa/MUb = -1, MUa=MUb).  If she has more anchovies, her MU for anchovies will diminish and if she has fewer biscuits, her MU for biscuits will rise.  That means her MRS will be less than -1.  If she has to trade biscuits for anchovies at a one-for-one ratio, her utility would fall. So she won’t make the trade.   Remember the MRS is at a point on the indifference curve.  Any deviation from that point changes her MRS. 

 

 

18.  Linda’s utility function for shoes S and the number of times she goes out dancing per month T is U(S,T) = 2ST.  It costs Linda $50 to buy one new pair of shoes or to spend an evening out dancing.  She has $500 to spend.

a.  The equation for her budget line is $500 = 50S + 50 T.  She can buy a maximum of 10 shoes and no dancing or 10 dancing trips and no shoes.

b.  Her MRS  is MUs/MUt=  -(∂U/∂S)/ (∂U/∂T) = -2T/2S = -T/S.

c.  Her optimal bundle is where MRS = MRT .  MRT = -Ps/Pt = -50/50 = -1

MRS (from (b) =-T/S    so –T/S = -1.  Therefore T=S and 500 = 50S + 50S   and 500 =100S and S = 5 and T = 5.

 

 

 

My questions:

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5

 

 

 

 

 

 

 

 

 

Car Washes

 

2.  Most of the time, a consumer can purchase as much of a good as she wants at an unchanged price.  Sometimes, however, we can get a discount for multiple purchases.  Suppose Julia can pay $10 to wash her car five times but if she washes her car more than five times, she is only charged $5 per car wash for more than 5 washes.  What does her budget line look like (draw it and explain it) if car washes is on one axis and all other goods on the other axis?

 

The budget line has a slope of -10 (assuming the CG (all other goods) costs $1) up to the point where she has 5 car washes.  After 5, the slope of the budget line is half of -10, or -5.  We don’t know what the X axis intercept is because we don’t know her income.

 

 

 

 

 

 

 

3.  The National Highway Transportation Safety Administration (NHTSA—pronounced nitsa) required front air bags in cars in 1997.  But air bags had been available as early as the 1970s and were widely available by the mid to late 1980s.   Consumers were aware that air bags saved lives and reduced injuries, yet many did not purchase them.  Can you explain this or must we assume consumers were not behaving rationally? (Hint:  They were rational so I won’t accept that as an answer.)

 

If we draw a budget line with air bags and the composite good then there must have been a corner solution for the consumers who did not purchase air bags.  The consumer below chooses not to buy air bags.

 

 

 

 

4.  You can buy newspapers and candy bars from (different) vending machines.  Use the concept of dimishing marginal utility to explain why newspaper vending machines allow you to open the box and essentially do not limit the number of newspapers you are able to take out of the machine while candy bar vending machines only dispense one candy bar at a time. 

 

Most people get utility from one newspaper but the MU you get from having 2 newspapers is low, or 0.  Therefore, you only take one out of the machine even though you could take more.  If the same held true for a candy bar machine, most people would probably take a lot of candy bars since the MU of the second candy bar is less than the first, but certainly not zero.