Question

1. Suppose that in a city there are 100 identical stores selling the same product. The total daily market demand function for the produce in the market is                              

QD =300,000 – 10,000P, where P is expressed in dollars per unit. The daily market supply curve is

QS = -15,000 + 20,000P

1. Determine algebraically the equilibrium price and quantity of product.
2. Now suppose the market is monopolized (e.g., a cartel is that determines price and quantity as a monopolist would). Determine the monopolist’s profit-maximizing price and quantity.
3. What is the dead weight loss (DWL)? (20 points)

• To work part b:

1. Find reverse demand curve (to put it in $)
2. Find MR curve (double reverse demand slope coefficient)
3. Find reserve supply curve (it is the marginal cost)
4. Set MR = MC and solve

• To work part c, dead-weight loss triangle is ½(base x height)

1. Base is difference between monopoly and competitive quantities
2. Height is difference between price and marginal cost (supply price) at the quantity where MR = MC.

Reference diagram on p. 405. It shows the idea of a DWL triangle but unlike the diagram, this problem has upsloping MC/S curve. You must calculate the MC to find the triangle. The difference between the demand price and the MC (the supply price) will be height of the DWL triangle.

Answer 1

(a)

Setting QD = QS,

300,000 - 10,000P = - 15,000 + 20,000P

30,000P = 315,000

P = 10.5

Q = - 15,000 + 20,000 x 10.5 = - 15,000 + 210,000 = 195,000

(b)

From demand function: P = (300,000 - QD) / 10,000

TR = P x QD = (300,000QD - QD2) / 10,000

MR = dTR/dQD = (300,000 - 2QD) / 10,000

From supply function: P = (QS + 15,000) / 20,000 = MC

Setting MR = MC and QD = QS,

(300,000 - 2Q) / 10,000 = (Q + 15,000) / 20,000

(300,000 - 2Q) = (Q + 15,000) / 2

600,000 - 4Q = Q + 15,000

5Q = 585,000

Q = 117,000

P = (300,000 - 117,000) / 10,000 = 183,000 / 10,000 = 18.3

(c)

DWL = (1/2) x Change in P x Change in Q

= (1/2) x (18.3 - 10.5) x (195,000 - 117,000)

= (1/2) x 7.8 x 78,000

= 304,200