Answer: See explanation below for answer.
Explanation:
a) In equilibrium the quantity supplied will equal the quantity demanded in all three markets. Algebraically this implies:
Qd S = Qs S
Qd A = Qs A
Qd T = Qs T
Substituting in the given curves implies:
1200 - 4PS + PA + PT = 4PS
1200 - 4PA + PS + PT = 4PA
1200 - 4PT + PS + PA = 4PT
Solving the first equation for PT and substituting into the second equation implies:
1200 - 4PA + PS + (8PS - PA - 1200) = 4PA
9PS = 9PA
Cancel 9 on both sides, we have:
=> PS = PA
Substituting these results into the third equation implies:
1200 - 4(8PA - PA - 1200) + PA + PA = 4(8PA - PA - 1200)
=> 10800 = 54PA
=> PA = 200
At:
PA = 200
PS = 200
PT = 200
The equilibrium quantities are:
QA = 800
QS = 800
QT = 800
b) Substituting the new supply curve for steel into the equilibrium condition, we have:
1200 - 4PS + PA + PT = PS
1200 - 4PA + PS + PT = 4PA
1200 - 4PT + PS + PA = 4PT
Again solving for PT in the first equation and substituting into the second equation, we have:
1200 - 4PA + PS + (5PS - PA - 1200) = 4PA
=> 6PS = 9PA
=> PS = 1.5PA
Substituting these results into the third equation, we have:
1200 - 4(5(1.5PA) - PA - 1200) + 1.5PA + PA = 4(5(1.5PA) - PA - 1200)
=> 10800 = 49.5PA
=> PA = 218.18
At:
PA = 218.18
PS = 327.27
PT = 218.18
At these prices, the equilibrium quantities are:
QA = 872.72
QS = 327.27
QT = 872.72
The shift in the supply of steel raises the equilibrium price for all three goods, lowering the equilibrium quantity of steel and raising the equilibrium quantities of aluminum and titanium. This last effect comes as a result of the demand curves for aluminum and titanium increasing in response to the shift in the steel supply curve.
c) Returning to the original equilibrium, this shift in the demand for aluminum implies:
1200 - 4PS + PA + PT = 4PS
1500 - 4PA + PS + PT = 4PA
1200 - 4PT + PS + PA = 4PT
Solving the first equation for PT and substituting into the second equation, we have:
1500 - 4PA + PS + (8PS - PA - 1200) = 4PA
=> 9PS + 300 = 9PA
=> PS = PA - 33.33
Substituting these results into the third equation, we have:
1200 - 4(8(PA - 33.33) - PA - 1200) + (PA - 33.33) + PA = 4(8(PA - 33.33) - PA - 1200)
=> 12900 = 54PA
=> PA = 238.89
At:
PA = 238.89
PS = 205.56
PT = 205.56
At these prices, the equilibrium quantities are:
QA = 955.56
QS = 822.24
QT = 822.24
An increase in the demand for aluminum will raise the equilibrium prices and quantities in all three markets. The price and quantity in the steel and aluminum industries increase because as the price of aluminum rises, the demand for steel and titanium increases.
