Question

In this question, assume that all variables other than price and quantity are held constant.

Answer 1

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.