Question

he market demand and supply functions for pizza in Newtown were QD = 10,000 - 1,000 P QS = -2,000 + 1,000 P Determine algebraically the equilibrium price and quantity of pizza and plot the market demand and supply curves, label the equilibrium point E, and draw the demand curve faced by a single pizza shop in this market on the assumption that the market is perfectly competitive. Show also the marginal revenue of the firm on the figure.

Answer 1

Answer

The market demand functions for pizza in Newtown is,

QD = 10,000 - 1,000P.................(1)

The market supply functions for pizza in Newtown is,

QS = - 2,000 + 1,000P................(2)

When market is in equilibrium, QD = QS

  10,000 - 1,000P = - 2,000 + 1,000P

Or,  - 1,000P - 1,000P = - 2,000 - 10,000

Or, - 2,000P = - 12,000

Or, P = - 12,000 / - 2,000

Or, P = 6

The equilibrium price of pizza in Newtown is $6.

Now, putting the value of P in equation(1), we get,

QD = 10,000 - 1,000 * 6

Or, QD = 10,000 - 6,000

Or, QD = 4,000

Again, putting the value of P in equation(2), we get,

QS = - 2,000 + 1,000 * 6

Or, QS = - 2,000 + 6,000

Or, QS = 4,000

  QD = QS = 4,000

  The equilibrium quantity of pizza in Newtown is 4,000.

The demand - supply schedule of pizza is shown in the following table;

Price	Quantity Demanded = 10,000 - 1,000P	Quantity Supplied = - 2,000 + 1,000P
0	10,000	-2,000
2	8,000	0
4	6,000	2,000
6	4,000	4,000
8	2,000	6,000
10	0	8,000

The market demand and supply curves are shown in the following figure.

In the above figure, the point 'E' shows the equilibrium point in pizza market.

The following figure shows the demand curve faced by a single pizza shop in this market on the assumption that the market is perfectly competitive. The figure also shows the marginal revenue(MR) curve of the firm/shop.

The second part of the above figure shows the demand curve of a single pizza shop in the market. Here the price is measured on the vertical axis and the quantity of pizza produced by a single pizza shop is shown on the horizontal axis. The shop takes the market price $6 as given. At this market price, the pizza shop faces a horizontal demand curve 'D' in the market.

The total revenue(TR) of the firm or shop is as follows,

TR = Price * quantity of pizza the firm sales(Q)

Or, TR = 6 * Q

MR = Marginal revenue = Change in TR / Change in output sold = d(TR) / dQ

Differentiating TR with respect to 'Q', we get,

d(TR) / dQ = d(6Q) / dQ

Or, MR = 6

At the given market price of pizza, the firm's revenue equals the price of pizza. Thus, the MR curve coincides with the demand curve, the firm or shop faces in the market. So, the MR curve of the firm equals the demand curve of the firm.

In the second part of the above figure, at the given market price of $6, the firm faces a horizontal demand and marginal revenue curve. Both the demand curve and the marginal revenue curve are same.

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