Question

Please answer all questions clearly with steps explained

Steve sells potatoes for his farm. His short-run cost function for potatoes is given by C(q) = q2 + 25q + 144

a. What is the price that will provide Steve zero profits?

b. If the price is below the level you found in part (b), will Steve shut down? If so, explain. If not, below what price will he shut down?

Answer 1

A) Steve will make zero profits or he will break even if he produces at the minimum point on the ATC. When AC is at it's minimum, AC = price = MC and therefore, Total Revenue = Total cost and profit will be zero.

Given that, TC = q² + 25q + 144

ATC = (TC/q) = q + 25 + (144/q)

When ATC is minimized, d(ATC)/dq = 0

Or, 1 + 0 -(144/q²) = 0

Or, (144/q²) = 1

Or, q² = 144

Or, q = 12

When q = 12, ATC = 12 + 25 + (144/12) = 49

Therefore, the price will be $49 at which Steve will make zero profits.

b) Steve will shut down only if in the short run, the market price falls below his minimum average variable cost of production because P < AVC means Total Revenue < total variable cost. Steve will shut down in this case because he won't be able to cover even his variable costs.

Steve's TVC = q² + 25q

Or, AVC = TVC/q = q + 25

Therefore, minimum AVC = $25

Steve will shut down only if the price is below $25.