Question

The demand function for good X is as follows: Qdx = -Px + 4Py + 3Y

(a) If Py = €500 and Y = €10,000 what is the demand function for good X?
(b) The supply function for good X is as follows: Qs = -10,000 + P. Using this function and the demand function you derived in part (a) calculate the equilibrium price and quantity of good x. Show your calculations.
(c) Draw the demand and supply curve and illustrate the equilibrium price and quantity. Illustrate the value of the intercepts on the demand curve and the intercept of the supply curve on the price axis. Please draw your diagram to an accurate scale.
(d) What is the demand function for good x when income increases to €12,000 and the price of good y remains constant at €500? Using this demand function and the supply function above, calculate the new equilibrium price and quantity.
(e) Draw the new demand curve on the diagram you drew in part (c) and illustrate the new equilibrium price and quantity. Illustrate the value of the intercepts on the new demand curve.

Answer 1

The demand function for good X can be found by substituting the given values of Py and Y into the demand function equation. The equilibrium price and quantity of good X can be found by setting the demand function equal to the supply function and solving for P and Q. The new demand function for good X when income increases can be found by substituting the new value of Y into the demand function equation.

Step-by-step explanation:

(a) To find the demand function for good X, we substitute the given values of Py and Y into the demand function equation: Qdx = -Px + 4Py + 3Y. Substituting Py = €500 and Y = €10,000, we have Qdx = -Px + 4(500) + 3(10,000). Simplifying, we get Qdx = -Px + 2,000 + 30,000. Combining like terms, the demand function for good X is Qdx = -Px + 32,000.

(b) To find the equilibrium price and quantity of good X, we set the demand function equal to the supply function: -Px + 32,000 = -10,000 + P. Solving for P, we get P = €6,000. Substituting this value of P into the demand function or the supply function, we can find the equilibrium quantity. Substituting into the demand function, we have Qdx = -€6,000 + 32,000 = 26,000. So the equilibrium price is €6,000 and the equilibrium quantity is 26,000.

(c) To draw the demand and supply curves, we plot the points (Qdx, Px) and (Qs, Px) respectively. The slope of the demand curve is -1 and the slope of the supply curve is 1. The demand curve intersects the y-axis at 32,000 and the supply curve intersects the x-axis at 10,000. The equilibrium point is where the demand and supply curves intersect.

(d) To find the new demand function when income increases to €12,000 and the price of good y remains constant at €500, we substitute the new value of Y into the demand function equation: Qdx = -Px + 4Py + 3Y. Substituting Py = €500 and Y = €12,000, we have Qdx = -Px + 4(500) + 3(12,000). Simplifying, we get Qdx = -Px + 2,000 + 36,000. Combining like terms, the new demand function for good X is Qdx = -Px + 38,000.

(e) To draw the new demand curve on the diagram, we plot the points (Qdx, Px) using the new demand function. The slope of the new demand curve is still -1, but the intercept on the y-axis is now 38,000. The new equilibrium price and quantity can be found by setting the new demand function equal to the supply function and solving for P and Q. This will give us the new equilibrium price and quantity.