Answers: Assignment 3

Econ. 103, Fall 2002, Prof. Nancy Folbre

Graphically:

4.15 The information provided implies an increase in the quantity of Tofu sold in the US over the time frame described, since both demand and supply have increased. Nothing can be inferred about the price however, as it could have increased or decreased, depending on the relative changes in supply and demand and the elasticity of both curves. The following graphics exemplify both possibilities:

1. Price Increase:

2. Price Decrease:

So it can be seen that the more supply increase relative to demand, all else equal, the lower the price will be. Moreover, the more elastic demand is, the less an increase in demand increases the price, and the more elastic supply is, the less an increase in supply engenders a decrease in price (it may be a good exercise to play around with curves of different elasticities yourself in order to ascertain the latter claim).

5.2 Tom should have three pizzas and two movies. There are many ways to derive this result, some more mathematically intensive than others, but here is an intuitive way to do so:

1. Equate Pizzas and Movies in money term; 1 pizza=2 movies, since the money required to buy a pizza is the same as the one needed to rent two movies.
2. Compare the utility gotten across bundles of the same value (1 p or 2 m) and then proceed to allocate the budget one bundle at a time:
• The first bundle of movies gives more utils than the first pizza, so get the movies first;
• Going along with this methodology, it can be seen that the increment in utility from getting 2 more movies (8), is lower than the one gotten from an increase in pizza consumption (20, then 18, then 16), so the remaining 18 dollars should be spent on pizza.

This works most of the time. The only thing to be wary about is the cases when it could be preferable not to spend the whole budget. So for insurance, always check whether dividing up bundles and not spending all is not better than spending everything when you get near the budget limit.

 

5.4



b) P=-(1/3000)Q+6

c) at P=3, the elasticity is E=(1/slope)(P/Q)=(1/(1/3000))(3/9000)=1;

d) Revenue is R=P*Q;

• at P=3, R=3*9000=27000
• at P=4, R=4*6000=24000

so the change in price would bring a decrease of 3000$ in revenues.

e) at P=2, the elasticity is E=(1/slope)(P/Q)=(1/(1/3000))(2/12000)=1/2;

f)

• at P=3, R=3*9000=27000
• at P=2, R=2*12000=24000

So the increase in price would increase revenues by 3000$.

g) at P=3, we have a unit elasticity, so for any P<3, the demand curve is inelastic, and for any P>3, it is elastic. Quick trick: when the demand curve is a straight line, the unit elasticity point is always in the middle of it (at P=b/2 and Q=-b/2m, for P=mQ+b).