Question

1. The market demand curve for a product is D(p) = q = 400 – 0.5p. The market supply curve is S(p) = q = 4p – 100.
a. Find the inverse demand & supply curves. (2 point)
b. Calculate the market equilibrium price & quantity. (2 points)
c. Draw a graph depicting these curves & the market equilibrium price & quantity. (3 points)

2. A competitive firm has the following cost function: c(y) = 4y² + 300.

a. What is their fixed cost and how do you determine it? (1 point)
b. Same cost function: c(y) = 4y² + 300. At what quantity is average total cost minimized? Why? (2 points)

Answer 1

a) Inverse demand is 0.5p = 400 - q or p = 800 - 2q.

Inverse supply function is 4p = q + 100 or p = 25 + 0.25q

b) Market equilibrium has qs = qd or 400 - 0.5p = 4p - 100 or 4.5p = 500.

Hence p = 500/4.5 = $111.11 per unit and q = 344.44 units.

This is the equilibrium price and quantity

c) Graph is shown below

2) a) Fixed cost is constant value independent of output.

Here the only constant is 300 so fixed cost is 300

b) ATC is C/y or 4y + 300/y. Now ATC is minimum when ATC'(y) = 0 which gives 4 - 300/y^2 = 0. This results in y = 8.66. Hence, ATC is minimum when y is 8.66 units