Temple University
Economics 615
Demand for Bread and Meat: Answer Key
1.a.
Q_{B} = 
1.95423 + 
.029601 Y + e 

(.842) 2.321 
(.00852) 3.47 
1.b.
Q_{B} = 
.4011 + 
.0245 Y + 
.4129 S  
.355 P_{B} 
+.57 P_{M} + e 

(1.03) .39 
(.00789) 3.10 
(.112) 3.69 
(.062) 5.73 
(.161) 3.54 
2.
t_{obs} = 1.954/.842 = 2.32 
P(2.32 < t < 2.32) @ .974 Therefore reject the null. 
3. i.




The observed F is above the critical value for any reasonable significance level, so reject the null. 
3.ii.

t_{obs} = .57/.161 = 3.53 

4.
i. 



ii. 



iii. 





iv. 




5. For the meat equation when the observations with Q_{m}=0 are omitted
Q_{M} = 
7.512 + 
.0389 Y  
.356 S + 
.146 P_{B}  
1.179 P_{M} + 
e 

(.95) 7.91 
(.008) 4.86 
(.121) 2.94 
(.061) 2.39 
(.149) 7.91 

When all the observations are used
Q_{M} =  7.815 +  .0411 Y   .4367 S +  .1625 P_{B}   1.2293 P_{M} +  e 
(1.045) 7.47 
(.008) 5.13 
(.114) 3.83 
(.063) 2.56 
(.163) 7.54 
a.
Delete Obs for which Q_{m}=0  All Observations 
At the 2.5% level reject Ho 
b.
Exclude obs for which Qm = 0  All observations 


Define 
.1625+.0411(4.7719)=.3586 
t_{obs} = 6.306 Reject the null. 
.0635^{2}+(4.7719)^{2}(.008)^{2}+2(4.7719)(.0002416)
=.003184 t_{obs} = 6.355 
6. Your answers to the meat part of this question will depend on how you dealt with the zeros in Q_{M}. The choices are to delete those observations; inadvisable since you lose valuable information. When Q_{M} = 0, let ln(Q_{M}) = 0; inadvisable since you are saying that these households are equivalent to those that consumed Q_{M} = 1. When Q_{M} = 0, reset it to Q_{M} = (some small number); inadvisable since this will tilt the regression line unduly. Add 1 to every observation on Q_{M}; best idea yet, although households with low Q_{M} experience a bigger % shift than those with high Q_{M}. You should read the text or lecture notes to decide how best to deal with missing data.
Results when observations corresponding to Q_{m} = 0 are deleted from both the Bread and Meat samples:  
LnQ_{B} = 
.5633 (.465) 
+.719 lnY (.162) 
+.33 ln S (.132) 
1.196 ln P_{B} (.172) 
+.066 ln P_{M} (.16) 
+ e 
LnQ_{M} = 
1.833 (1.54) 
+1.514 lnY (.54) 
+.899 ln S (..44) 
+.642 ln P_{B} (.57) 
2.282 ln P_{M} (.54) 
+ e 
Use all data for bread and add 1 to Q_{m}.  
LnQ_{B} = 
.6433 (.4207) 
+.7057 lnY (.1319) 
+.37 ln S (.1075) 
1.1428 ln P_{B} (.1555) 
+.6303 ln P_{M} (.1555) 
+ e 
LnQ_{M} = 
.8025 
+1.213 lnY 
.847 ln S 
+.5087 ln P_{B} 
1.782 ln P_{M} 
+ e 
a.


All observations  Delete obs for which Qm = 0 


t_{obs} = .07581/.09958 = .76126 
t_{obs} = .761 
b.



1.213.84711 = .6341

t_{obs} = 1.041 
t_{obs} = 2.33 