Question

Problem 1. Suppose global demand in the perfectly competitive yoga mat industry is characterized by the following function: Q_D=490,000-1,000P. Suppose the typical yoga mat manufacturer has a short-run total cost curve characterized by STC = 0.01q² - 8q+9, so SMC = 0.02q-8.

1. (4 points) Calculate the typical firm's short-run average cost function. At what level of output does short-run average cost reach a minimum?

2. (4 points) Calculate the short-run supply curve for the typical firm and the industry short-run supply curve. Assume that there are currently 1000 yoga mat manufacturers in the industry.

3. (2 points) Find the price at which the typical firm will shut down.

4. (bonus: 2 points) Graph the typical firm's short-run marginal cost and marginal revenue functions, indicating the equilibrium output, price, and profit on your graph.

Answer 1

1)STC = 0.01q2 + 8q+9

ATC=STC/q=0.01q+8+9/q

AC is Minimum at where it is equal to MC

0.01q+8+9/q=0.02q+8

9/q=0.01q

9/0.01=q^2

Q=√900=30

So at Q=30 ,AC is at minimum

B) Supply Curve of a typical perfect competition firm is nothing but Marginal cost.

So ,

Supply Curve,

P=0.02q+8

Qs=50p-400{ typical firm supply curve}

Industry supply curve,

Qs=1000(50p-400)=50,000p-400,000

C) typical firm will shut down at,

P≤AVC

TVC=0.01q2+8q

AVC=0.01q+8

At q=30( long run typical firm output),

AVC=0.01*30+8=8.3

P≤8.3 ,will lead firm to shutdown .