Exercise 2.1
y=25
t=0.01 per block
x=? commuting distance in blocks.
q=1,500
Budget constraint: c + pq= y−tx
c +1500 p=25−0.01 x
Since housing consumption is fixed at 1,500, the only way that utilities can be equal for all urban
residents is for bread consumption c to be the same at all locations. The consumption bundle (the
bread, housing combination) will then be the same at all locations, yielding equal utilities.
For c to be constant across locations, the price per square foot of housing must vary with x in a way
that allows the consumer to afford a fixed amount of bread after paying his rent and his commuting
cost.
A.
¿
c +1,500 p=25−0.01 x
1,500 p=25−0.01 x −c ¿
¿
25−0.01 x−c
p=
1500
¿
c is fixed, so the numerator can only variate by changing x (number of blocks away from the CBD). If
x increases, the price per square foot would decrease (and the other way around), as the numerator
will be smaller than initially. Which implies an negative (inverse) correlation.
B.
Profit=15,000 p−90−r
r =land rent per square block
In equilibrium, land rent adjusts so that this profit is identically zero. So:
r =15,000 p−90
15,000∗25−0.01 x−c¿
r= −90
1500
( 375,000−150 x −15,000 c¿ )
r= −90
1,500
¿
r =250−0.1 x−10 c −90
¿
r =160−0.1 x−10 c
y=25
t=0.01 per block
x=? commuting distance in blocks.
q=1,500
Budget constraint: c + pq= y−tx
c +1500 p=25−0.01 x
Since housing consumption is fixed at 1,500, the only way that utilities can be equal for all urban
residents is for bread consumption c to be the same at all locations. The consumption bundle (the
bread, housing combination) will then be the same at all locations, yielding equal utilities.
For c to be constant across locations, the price per square foot of housing must vary with x in a way
that allows the consumer to afford a fixed amount of bread after paying his rent and his commuting
cost.
A.
¿
c +1,500 p=25−0.01 x
1,500 p=25−0.01 x −c ¿
¿
25−0.01 x−c
p=
1500
¿
c is fixed, so the numerator can only variate by changing x (number of blocks away from the CBD). If
x increases, the price per square foot would decrease (and the other way around), as the numerator
will be smaller than initially. Which implies an negative (inverse) correlation.
B.
Profit=15,000 p−90−r
r =land rent per square block
In equilibrium, land rent adjusts so that this profit is identically zero. So:
r =15,000 p−90
15,000∗25−0.01 x−c¿
r= −90
1500
( 375,000−150 x −15,000 c¿ )
r= −90
1,500
¿
r =250−0.1 x−10 c −90
¿
r =160−0.1 x−10 c
