1.(a) The demand curve for butter in Dammam is given as Q(D)=300-2P+4I and the supply curve of butter in Dammam is Q(S)=3P-25P(m)-25 where Q(D) and Q(S) denote the quantity demanded and supplied of milk respectively and the P and P(m) represented the price of butter and price of milk respectively. Based on the market equilibrium condition or principle the market demand is equal or identical to the market supply for any good or service.

Therefore, based on the market equilibrium condition or principle, when I=25 and P(m)=1, it can be stated:-

Q(D)=Q(S)

300-2P+4I=3P-25P(m)-25

300-2P+4*(25)=3P-25(1)-25

300-2P+100=3P-25-25

400-2P=3P-50

-3P-2P=-400-50

-5P=-450

P=-450/-5

P*=90

Hence, the equilibrium price of butter or P* is 90 when I=25 and P(m)=1.

Now, plugging the value of P* and I into the supply function of butter, we get:-

Q(S)=300-2P+4I

Q(D)=300-2*(90)+4*(25)

Q(D)=300-180+100

Q(D)=400-180

Q*=220

Thus, the equilibrium quantity of butter in the butter market in Dammam is 220 units.

(b) Now, due to the bad weather conditions, the price of milk increases to 2 implying that P(m)=2 now and the income or I remains unchanged at 25.

Therefore, again based on the market equilibrium condition when I=25 and P(m)=2, we get:-

Q(D)=Q(S)

300-2P+4I=3P-25P(m)-25

300-2P+4*(25)=3P-25(2)-25

300-2P+100=3P-50-25

400-2P=3P-75

-3P-2P=-400-75

-5P=-475

P=-475/-5

P*=95

Hence, the equilibrium price of butter or P* is 95 when I=25 and P(m)=1.

Now, plugging the value of P* and I into the supply function of butter, we get:-

Q(S)=300-2P+4I

Q(D)=300-2*(95)+4*(25)

Q(D)=300-190+100

Q(D)=400-190

Q*=210

Thus, the equilibrium quantity of butter in the butter market in Dammam now becomes 210 units.

Figure-1 in the document attached below illustrates the impact of an increase in milk price on the butter market in Dammam. Considering the initial values of I and P(m), the initial market demand curve and supply curve of butter are denotes as D1 and S1 respectively and the equilibrium price and quantity of butter in the market are 90 ad 220 units respectively corresponding to the intersection of D1 and S1 curves at point E1. Now, due to the bad weather conditions as P(m) falls the market supply of butter decreases as indicated by an upward or leftward shift of the the market supply curve from its initial position S1 to S2 and the new equilibrium price and quantity of butter now become 95 and 210 units respectively corresponding to the intersection of S2 and D1 curves at point E2.

(c) In this case, P=100, I=25, and P(m)=1.

Now, plugging these respective values into the demand function for butter, we would get:

Q(D)=300-2P+4I

Q(D)=300-2*(100)+4*(25)

Q(D)=300-200+100

Q(D)=200

Now, note that in this instance dQ(D)/dP=-2 and P/Q=100/200=1/2=0.5. Now, based on the mathematical formula to calculate the own price elasticity of demand, the own price ealsticity of demand of any good or service=dQ(D)/dP*(P/Q).

Hence, using the mathematical formula to calculate the own price elasticity of demand, we can state, in this case:-

-dQ(D)/dP*(P/Q)

=(-2)*(0.5)

=-1

Thus, the own price elasticity of demand of butter, in this case, would be -1.

(d) Now, P=100, P(m)=1, and I=25

Now, plugging these respective values into the demand function for butter, we would get:

Q(D)=300-2P+4I

Q(D)=300-2*(100)+4*(25)

Q(D)=300-200+100

Q(D)=200

Note that dQ(D)/dI=4 and I/Q=25/200=1/8. In this instance, based on the mathematical formula to calculate the income elasticity of demand, it can be stated that income elasticity of demand would be=dQ(D)/dI*I/Q

Hence, using the mathematical formula to calculate the income elasticity of demand, we can state, in this case:-

dQ(D)/dI*(I/Q)

=(4)*(1/8)

=1/2 or 0.5

Thus, the income elasticity of demand of butter, in this case, would be 1/2 or 0.5

(e) In this case, P=100, P(m)=4

Now, plugging these respective values into the supply function for butter, we would get:

Q(S)=3P-25P(m)-25

Q(D)=3*(100)-25*(4)-25

Q(D)=300-100-25

Q(D)=175

Note that dQ(S)/dP=3 and P/Q=100/175=0.57. In this instance, based on the mathematical formula to calculate the own price elasticity of supply, it can be stated that price elasticity of supply would be=dQ(S)/dP*P/Q

Hence, using the mathematical formula to calculate the price elasticity of supply, we can state, in this case:-

dQ(S)/dP*(P/Q)

=(3)*(0.57)

=1.71

Thus, the own price elasticity of supply of butter, in this case, would be 1.71

(f) In this case, P=100, P(m)=10

Now, plugging these respective values into the supply function for butter, we would get:

Q(S)=3P-25P(m)-25

Q(D)=3*(100)-25*(10)-25

Q(D)=300-250-25

Q(D)=25

Note that dQ(S)/dP(m)=-25 and P(m)/Q=10/25=2/5. In this instance, based on the mathematical formula to calculate the cross price elasticity of supply, it can be stated that cross elasticity of supply would be=dQ(S)/dP(m)*P(m)/Q

Hence, using the mathematical formula to calculate the cross price elasticity of supply, we can state, in this case:-

dQ(S)/dP(m)*(P(m)/Q)

=(-25)*(2/5)

=-10

Thus, the cross price elasticity of supply of butter, in this case, would be -10

2 (a) i. The domestic demand function of butter in butter market in Saudi Arabia is given as Q(D)=10-2P and the supply curve of butter in Saudi Arabian butter market is given as Q(S)=2P-2. The price ceiling in the market is set at 2.

Therefore, plugging the value of price ceiling into the demand function, we get:-

Q(D)=10-2P

Q(D)=10-2*(2)

Q(D)=10-4

Q(D)=6

Thus, the quantity demanded of butter at the price ceiling of 2 is 6 units.

Again, plugging the value of price ceiling into the supply function of butter, we get:-

Q(S)=2P-2

Q(S)=2*(2)-2

Q(S)=4-2

Q(S)=2

Hence, the quantity supplied of butter at the price ceiling of 2 is 2 units.

Therefore, the overall shortage or excess demand of butter in the Saudi Arabian market, in this case=(6 units-2 units)=4 units.

(ii) Based on the market equilibrium condition, it can be stated:-

Q(D)=Q(S)

10-2P=2P-2

-2P-2P=-10-2

-4P=-12

P=-12/-4

P*=3

Thus, the equilibrium price of butter in the Saudi Arabian market is 3

Now, plugging the value of P* into the demand function of butter, we obtain:-

Q(D)=10-2P

Q(D)=10-2*(3)

Q(D)=10-6

Q*=4

Hence, the equilibrium quantity of butter in the Saudi Arabian market is 4 units.

Now, when Q(D)=2 the price that consumers in the butter market willing to pay would be:-

Q(D)=10-2P

2=10-2P

-10+2=-2P

-8=-2P

-8/-2=P

4=P

Therefore, when Q(D)=2 the price that the butter consumers are willing to pay in Saudi Arabian market would be 4.

Thus, the deadweight loss in the market created due to the price ceiling, in this case=(0.5)*(4-2)*(4-2)=0.5*2*2=2

(b)i. Now, the government imposes a per unit tax on butter supply of $1the price that the butter consumers would pay is=(P*+0.5)=(3+0.5)=3.5 and the price received by the butter suppliers=(P*-0.5)=(3-0.5)=2.5.

Now, when Q(D)=0 the quanity demanded of butter would become:-

Q(D)=10-2P

0=10-2P

-10=-2P

-10/-2=P

5=P

Thus, when the Q(D)=0 the price that the butter consumers are willing to pay is 5, in this case.

Now, when P=3.50, Q(D) would become:-

Q(D)=10-2P

Q(D)=10-2*(3.5)

Q(D)=10-7

Q(D)=3

Hence, the consumer surplus after the imposition of the per-unit tax on butter supply=0.5*(5-3.5)*(3-0)=0.5*(1.5)*(3)=2.25

ii. Now, when the P=2.5 the Q(S) would be:-

Q(S)=2P-2

Q(S)=2*(2.5)-2

Q(S)=5-2

Q(S)=3

Hence, when the P=2.5 the Q(S) becomes 3.

When Q(S)=0, the price charged by the butter suppliers in the market would be:-

Q(S)=2P-2

0=2P-2

2=2P

2/2=P

1=P

Thus, when Q(S) the price that the butter suppliers are willing to charge is 1.

Therefore, the producer surplus after the imposition of the per unit tax on butter supply=0.5*(2.5-1)*(3-0)=0.5*1.5*3=2.25

iii. The total government revenue collected after the imposition of the per-unit tax on butter=(3.5-2.5)*3=3

iv. The deadweight loss in the Saudi Arabian butter market due to the imposition of per-unit tax on butter supply=0.5*(3.5-2.5)*(4-3)=0.5*1*1=0.5

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