91影视

Let the demand curve be Q = a + bP_G + eP_O, where a is the intercept value, b is the change in the quantity of gas by change in the price of gas, e is the change in the quantity of gas by change in the price of oil.

The price elasticity of demand will be -0.5, cross-price elasticity of demand will be 1.5, gas price is $6.40, the quantity of gas 23 Tcf, and oil price is $50, given in Example 2.10 (Page 81).

The cross-price elasticity of demand is calculated below:

$$\begin{gathered} E_{GO}=\frac{鈻�Q}{鈻�P_O}脳\frac{P_O}{Q} \\ 1.5=\frac{鈻�Q}{鈻�P_O}脳\frac{50}{23} \\ \frac{鈻�Q}{鈻�P_O}=\frac{1.5脳23}{50} \\ e=0.69 \end{gathered}$$

The price elasticity of demand is calculated below:

$$\begin{gathered} E_D=\frac{鈻�Q}{鈻�P_G}脳\frac{P_G}{Q} \\ -0.5=\frac{鈻�Q}{鈻�P_G}脳\frac{6.40}{23} \\ \frac{鈻�Q}{鈻�P_G}=\frac{-0.5脳23}{6.40} \\ e=-1.8 \end{gathered}$$

The intercept value, i.e., a, is calculated below:

Q = a - 1.8P_G +0.69P_O

23 = a - 1.8(6.40) + 0.69(50)

23 = a - 11.52 + 34.5

a = 23 + 11.52 -34.5

a = 0.02

The demand curve will be Q = 0.02 鈥� 1.8P_G+ 0.69P_o.

Let the supply curve be Q = c + dP_G + fP_O, where c is the intercept value, d is the change in the quantity of gas by change in the price of gas, f is the change in the quantity of gas by change in the price of oil.

The price elasticity of supply will be 0.2, cross-price elasticity of supply will be 0.1, gas price is $6.40, the quantity of gas 23 Tcf, and oil price is $50, given in Example 2.10 (Page 81).

The cross-price elasticity of supply is calculated below:

$$\begin{gathered} E_{GO}=\frac{鈻�Q}{鈻�P_O}脳\frac{P_O}{Q} \\ 0.1=\frac{鈻�Q}{鈻�P_O}脳\frac{50}{23} \\ \frac{鈻�Q}{鈻�P_O}=\frac{0.1脳23}{50} \\ f=0.05 \end{gathered}$$

The price elasticity of supply is calculated below:

$$\begin{gathered} E_s=\frac{鈻�Q}{鈻�P_G}脳\frac{P_G}{Q} \\ 0.2=\frac{鈻�Q}{鈻�P_G}脳\frac{6.40}{23} \\ \frac{鈻�Q}{鈻�P_G}=\frac{0.2脳23}{6.40} \\ d=0.72 \end{gathered}$$

The intercept value, i.e., c, is calculated below:

Q = c - 0.05P_G +0.72P_O

23 = c + 0.72(6.40) + 0.05(50)

23 = c + 4.608 + 2.5

c = 23 - 4.608 - 2.5

c = 15.9

The supply curve will be Q = 15.9 + 0.72P_G + 0.05P_o.

Thus, the supply curve is Q = 15.90 + 0.72P_G + 0.05P_O, and demand curve Q = 0.02 - 1.8P_G + 0.69P_O; hence, proved.

The market price of gas when the price of oil is $50 is calculated below:

At equilibrium, demand is equal to supply.

D = S

0.02 - 1.8P_G + 0.69(50) = 15.90 + 0.72P_G + 0.05(50)

34.52 - 1.8P_G = 18.4 + 0.72P_G

1.8P_G + 0.72P_G = 34.52 - 18.4

2.52P_G = 16.12

P_G = $6.40

Thus, the price is $6.40.

The demand and supply at $4.50 are calculated below:

Q_D = 0.02 - 1.8(4.50) + 0.69(50)

= 0.02 - 8.1 + 34.5

= 26.38

Q_S = 15.9 + 0.72(4.50) + 0.05(50)

= 15.9 + 3.24 + 2.5

= 21.64

The demand is greater than supply; thus,the excess demand will be 4.74 Tcf(=26.38 鈥� 21.64).

The market price of gas when the price of oil is $100 is calculated below:

At equilibrium, demand is equal to supply.

D = S

0.02 - 1.8P_G + 0.69(100) = 15.90 + 0.72P_G + 0.05(100)

69.02 - 1.8P_G = 20.9 + 0.72P_G

1.8P_G + 0.72P_G = 69.02 - 20.9

2.52P_G = 48.12

P_G = $19.10

The price will be $19.10.