Answer:
A. The price reduced by 0.115%
B. Betty can expect her total revenue to increase.
C. The demand reduced by 43.32%
D. Patty can expect her total revenue to increase.
Explanation:
A.
The price elasticity of demand can be expressed as shown below;
P.E=%Q/%P
where;
P.E=price elasticity of demand
%Q=percentage change in the quantity demanded
%P=percentage change in price
In our case;
P.E=305
%Q=35%=0.35
%P=unknown, to be determined
Substituting;
305=0.35/P
305 P=0.35
P=0.35/305=0.00115
%P=0.0011×100=0.115%
The price reduced by 0.115%
B.
Determine the initial and final revenue and compare to illustrate if the revenue increased or reduced.
Initial Revenue=initial unit price×initial quantity demanded
where;
Initial unit price=p
Initial quantity=q
replacing;
Initial Revenue=p×q=pq
Final Revenue=final unit price×final quantity demanded
where;
final unit price=(p-0.115% of p)=p-0.00115 p=0.99885 p
final quantity demanded=(q+35% of q)=(q+0.35 q)=1.35 q
Substituting;
Final revenue=(0.99885 p)×(1.35 q)=1.348 pq
Final revenue-Initial revenue=1.348 pq-pq=0.348 pq
Betty can expect her total revenue to increase.
C.
Using the same expression as above;
P.E=%Q/%P
where;
P.E=0.57
%Q=unknown, to be determined=0.01 Q
%P=76%=76/100=0.76
Substituting;
0.57=0.01 Q/0.76
0.01 Q=0.57×0.76
Q=(0.57×0.76)/0.01
Q=43.32%
The demand reduced by 43.32%
D.
Initial Revenue=initial unit price×initial quantity demanded
where;
Initial unit price=p
Initial quantity=q
replacing;
Initial Revenue=p×q=pq
Final Revenue=final unit price×final quantity demanded
where;
final unit price=(p+76% of p)=p+0.76 p=1.76 p
final quantity demanded=(q-43.32% of q)=(q-0.43 q)=0.57 q
Substituting;
Final revenue=(1.76 p)×(0.57 q)=1.0032 pq
Final revenue-Initial revenue=1.0032 pq-pq=0.0032 pq
Patty can expect her total revenue to increase.