Consider a competitive industry and a price-taking firm that produces a certain product in that industry. The market pri

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Consider a competitive industry and a price-taking firm that
produces a certain product in that industry. The market price for
that product is $5 per unit. The manager estimates the average
variable cost function to be AVC = 5 - 0.0032Q + 0.0000008Q^2 Q^2
denotes Q squared Average variable cost (AVC) reaches its minimum
value at how many units of output? Hint: take the first derivative
of the AVC function, make it equal 0, and solve for Q. What is the
minimum value of average variable cost (AVC)? Hint: plug the answer
from question 1 back into the AVC function and solve for AVC.
Should the manager produce or shut down? Why? Hint: compare market
price with the minimum value of AVC you get from question 2. What
is the marginal cost (MC) function? Hint: get the Total Variable
Cost (TVC) function based on the AVC function, then take the first
derivative of the TVC function. What is the optimal level of
production for the firm? Hint: MR=MC, solve for quantity Q. Here MR
(marginal revenue) equals the market price.