Question

Consider a competitive industry and a price-taking firm that produces in that industry. The market demand and supply functions are estimated to be:

Demand: Q_d= 10,000 - 10,000P + 1.0M

Supply: Q_s= 80,000 + 10,000P - 4,000P₁

where Q is quantity, P is the price of the product, M is income, and P₁ is the input price. The manager of the perfectly competitive firm uses time-series data to obtain the following forecasted values of M and P₁ for 2015:

M̂ = $50,000 and P̂₁ = $20

The manager also estimates the average variable cost function to be

AVC = 3.0 - 0.0027Q + 0.0000009Q²

Total fixed costs will be $2,000 in 2015. The minimum value of average variable cost is $_____.

$0.50

$0.75

$0.975

$1.00

$2.15

Answer 1

AVC = 3.0 - 0.0027Q + 0.0000009Q²

dAVC/dQ=-0.0027+0.0000018Q

Put dAVC/dQ=0 for minimization

-0.0027+0.0000018Q=0

Q=0.0027/0.0000018=1500

We find that AVC is minimized at Q=1500.

Let us find the AVC at Q=1500.

Put Q=1500 in AVC function

AVC = 3.0-0.0027*1500+0.0000009*1500²=$0.975

Correct option is $0.975