Consider the market for trucks. Assume that the demand for trucks is given by
60 2 5 D Q P Y where P is price per truck and Y is the income of the buyers. The
supply of trucks is given by 30 5 3 S Q P W where W is the price of all the materials
needed to produce a truck. Solve for the equilibrium price P* and equilibrium quantity
Q* of trucks bought and sold. [10 marks]
4.
To solve for the equilibrium price and quantity of trucks bought and sold, we need to find the values that equate the quantity demanded and the quantity supplied.
Given:
Demand for trucks: D = 60 - 2P + 5Y
Supply of trucks: S = 30 + 5P - 3W
Equilibrium occurs when the quantity demanded (D) equals the quantity supplied (S). Therefore, we can set D equal to S and solve for P.
Setting D = S:
60 - 2P + 5Y = 30 + 5P - 3W
Now, we can rearrange the equation to isolate the price P:
7P = 30 - 60 - 3W + 2P - 5Y
Combine like terms:
5P = -30 - 3W - 5Y
Divide by 5:
P = (-30 - 3W - 5Y) / 5
So, the equilibrium price P* is given by the equation:
P* = (-30 - 3W - 5Y) / 5
To find the equilibrium quantity Q*, substitute the equilibrium price P* back into the demand or supply equation and solve for Q.
Using the demand equation D = 60 - 2P + 5Y:
Q* = 60 - 2P* + 5Y
Substituting the value of P*:
Q* = 60 - 2((-30 - 3W - 5Y) / 5) + 5Y
Simplify the equation:
Q* = 60 + 6W/5 + 10Y/5 + 5Y
Q* = 60 + (6W + 10Y)/5 + 5Y
Therefore, the equilibrium quantity Q* is given by the equation:
Q* = 60 + (6W + 10Y)/5 + 5Y
By substituting the values of W and Y into the equations for P* and Q*, you can find the numerical values of the equilibrium price and quantity of trucks bought and sold.