Question

Consider a competitive market for red lentils with 10,000 identical farmers, a competitive market price of $5 and the following ?? for each farmer:

MC = $0.5+ $0.05Q

Also consider the following market demand function:

QD=1,100,000-40,000P

a) Calculate the optimal level of production (in tonnes) for each farmer (show workings).

b)Assuming 10,000 lentil farmers of equal size, determine the market supply function and the equilibrium market quantity (show workings).   

c) Consider that the government now imposes a 25% tax on producers, calculate the new market equilibrium price (two decimal places) and new market equilibrium output (two decimal places) (show workings).

d)Calculate the value of the deadweight loss for the consumer and the producer following a 25% tax on red lentils, as well as, the amount of government revenue.

Answer 1

(a)

For each farmer, P = MC

0.5 + 0.05Q = 5

0.05Q = 4.5

Q = 90

(b)

Individual Firm supply function: P = MC

P = 0.5 + 0.05Q

As there are 10,000 farmers,

Market supply (QS) = 10,000Q

Q = QS / 10,000

P = 0.5 + 0.05 x (QS / 10,000)

0.05 x (QS / 10,000) = P - 0.5

QS / 10,000 = 20P - 10

QS = 200,000P - 100,000

Equating QD = QS,

1,100,000 - 40,000P = 200,000P - 100,000

240,000P = 1,200,000

P = 5

Q = 200,000 x 5 - 100,000 = 900,000

(c)

The tax decreases price received by sellers by 25% at every output level. New supply function is

QS1 = 200,000 x 0.75 x P - 100,000 = 150,000P - 100,000

Equating QD = QS1,

1,100,000 - 40,000P = 150,000P - 100,000

190,000P = 1,200,000

P = 6.32

Q = 150,000 x 6.32 - 100,000 = 848,000.00

(d)

When P = 6.32,

Tax per unit = 6.32 x 25% = 1.58

Deadweight loss = (1/2) x Tax per unit x Change in Q = (1/2) x 1.58 x (900,000 - 848,000) = 0.69 x 52,000 = 35,880

Tax revenue = 1.58 x 848,000 = 1,339,840