Question

Assume that demand for a commodity is represented by the equation P = 10 – 0.2 Q d, and supply by the equation P = 5+ 0.2 Qs where Qd and Q s are quantity demanded and quantity supplied, respectively, and P is the Price. Use the equilibrium condition Qs = Qd a. Solve the equations to determine equilibrium price b. Now determine the equilibrium quantity c. Graph the two equations to substantiate your answers and label these two graphs D1 and S1. 2. Furthermore; assume the demand for this product increases because of a change in income. a. Graph the new demand curve and label as D2 b. What will be the new equilibrium price and quantity compared to the initial one. c. Is this product normal good or inferior good?

Answer 1

Answer (a) - The inverse demand curve equation is given, P = 10 - 0.2Qd. We can write inverse demand function as Qd = 10/0.2 - (1/0.2)P

Or Qd = 50 - 5P

The inverse supply function is P = 5+0.2Qs. We can write this as Qs = (1/0.2)P - 5/0.2

Or, Qs = 5P - 25

The equilibrium price will be determined where Qd = Qs. Place both equation

50 - 5P =  5P - 25

75 = 10P

P = $7.5 per unit

This is equilibrium price of the commodity in the market.

(b) Now place value of equilibrium price in the demand equation in order to calculate equilibrium quantity.

Qd = 50 - 5*(7.5)

Qd = 50 - 37.5

Qd = 12.5 units

This is equilibrium quantity of the commodity in the market.

(c) - The graph has been given below.

Answer 2 (a) - Suppose demand for this product has increased because of change in income. Increase in income would shift demand curve to the right. New demand curve has been show by 'D2' in the given diagram.

(2b) - We can see in the diagram that equilibrium price and quantity have changed. New equilibrium price is (P*) and new equilibrium quantity is (Q*). Price and quantity both have risen due increase in the income.

(2c) - The good is a ''normal good''. Quantity demanded rises are income goes up of the consumer. In the market price and quantity both are raising, thus we have concluded that.