Question

Firms produce garden gnome lawn ornaments with a marginal private cost curve equal to MPC=40+Q. The production of lawn ornaments creates a marginal external cost equal to MEC=2Q. The demand for lawn ornaments is equal to Pd = 200 - Qd .

a) (5 points) In the space below, draw and label these curves. Be sure the intercepts are correct, but remember it doesn't have to be drawn perfectly to scale.

b) (2 points) Calculate the quantity and price of lawn ornaments if the market operates without intervention (market outcome). Label these values on the graph above.

c) (2 points) Calculate the quantity and price of lawn ornaments at the socially efficient outcome. Label these values on the graph above.

d) (2 points) Label the area that represents DWL on the graph above (you do not need to calculate it)

e) (2 points) Calculate the tax per unit that would induce the production of the socially efficient number of lawn ornaments.

Answer 1

(a)

Marginal social cost (MSC) = MPC + MEC = 40 + Q + 2Q = 40 + 3Q

From demand function, When Qd = 0, Pd = 200 (Vertical intercept) & when Pd = 0, Qd = 200 (Horizontal intercept).

From MPC function, When Q = 0, MPC = 40 (Vertical intercept)

From MEC function, When Q = 0, MEC = 0 (Vertical intercept)

From MSC function, When Q = 0, MEC = 40 (Vertical intercept)

In following graph, D (demand), MPC, MEC and MSC curves are drawn.

(b)

In market outcome, Demand = MPC.

200 - Q = 40 + Q

2Q = 160

Q = 80

P = 200 - 80 = 120

(c)

In social outcome, Demand = MSC.

200 - Q = 40 + 3Q

4Q = 160

Q = 40

P = 200 - 40 = 160

(d)

In above graph, DWL is area ABC.

(e)

When Q = 40, MEC = 2 x 40 = 80

Unit tax = MEC = 80