Econ Problem set 1

Econ Problem set 1 - Leo Spornstarr TA: Bridget Hoffman...

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Leo Spornstarr TA: Bridget Hoffman Microeconomics January 17, 2010 Econ Homework, Problem Set I 1a. there are a few general properties of all utility functions. That there are always increasing at a decreasing rate, yet it is impossible to accurately define how much it increases each time as it is a personal preference of how much an individual likes something. Doing some calculations can help us determine a few restrictions that we can put on U(2). It must be greater than 48 and less than 124. However, it cannot be 96 (48*2) because the first time it increased that much and the U function decreases as the x function increases, this is the upper limit. We also can determine that it must be greater than 86 though because 124-48 = 76/2 = 38 and since the U needs to be decreasing between increasing values; this finds us the lower limit. Therefore, 96 >U(2)>86. The same logic can be applied U(5). Since the difference between 152-124 = 28, U(5)> (196- 28), as once again the U function decreases as x increases. And then the difference between U(5) and 196 must be less than half of the difference between 196-152=44 44/2=22 in order to guarantee that U Is decreasing as x is increasing. Then 152+22=174, which is the lower limit. Therefore 180 > U(5) > 174. 1b. To figure out the price of coconuts we have to use the simple formula that when the utility is maxed out completely. MU(coconuts)/P(coconuts) = MU(muffins)/P(muffins). Using the numbers we know of mu(c)=42 (given), Mu(muffins) (M(u(4)-U(3))=28, P(m)=4. We substitute in 28/4 = 42/x. Do some algebra and we get the price of one coconut equal to $6. 1c. Biggie’s income level is equal to P(coconut)*#of coconuts bought + P(muffins)*#of muffins bought = Income. Doing some simple substitution and addition 6*3 + 4*4 = $34. His income level is equal to $34. 2a. The first thing to note is that we should note is that Income = Price of 1 * amount of 1 + price of 2 * amount of 2. Here we have waffles (x) and eggs (y). So we substitute what we know into the equation. 30 = P(y)*A(y) + P(x)*A(x). P(y)=2 and P(x)=3. 30 = 3A(x)+2A(y). To find out the opportunity cost of consuming an additional egg, we must find the equation of the
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Econ Problem set 1 - Leo Spornstarr TA: Bridget Hoffman...

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