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: $Q _ { d } = 10,000 - 10,000 P + 1.0 M$ Supply: $Q _ { s } = 80,000 + 10,000 P - 4,000 P _ { I }$ where Q is quantity,P is the price of the product,M is income,and $$P _ { I }$$ is the input price.The manager of the perfectly competitive firm uses time-series data to obtain the following forecasted values of M and $P _ { I }$ for 2021: $\hat { M } = \$ 50,000 \text { and } \hat { P } _ { I } = \$ 20$ The manager also estimates the average variable cost function to be $A V C = 3.0 - 0.0027 Q + 0.0000009 Q ^ { 2 }$ Total fixed costs will be $2,000 in 2021.The manager _____ produce since _____________.

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To determine whether the firm should produce, we need to compare the price at which the firm can sell its product with its average variable cost (AVC) at the equilibrium quantity. The equilibrium price can be found by setting the demand equal to the supply and solving for P. Using the forecasted values for M and $P_I$, we have:Demand: $Q_d = 10,000 - 10,000P + 1.0(50,000)$Supply: $Q_s = 80,000 + 10,000P - 4,000(20)$Simplifying these gives:Demand: $Q_d = 60,000 - 10,000P$Supply: $Q_s = 80,000 + 10,000P - 80,000$Supply simplifies to: $Q_s = 10,000P$Setting $Q_d = Q_s$ to find the equilibrium price:$60,000 - 10,000P = 10,000P$Solving for P gives: $20,000P = 60,000$, so $P = 3$.Given the AVC function $AVC = 3.0 - 0.0027Q + 0.0000009Q^2$, we need to compare this AVC at the equilibrium quantity with the price P = $3. However, without the equilibrium quantity, we directly compare the price to the initial AVC term, which is $3.0. Since the price the firm can sell its product for ($3) is greater than the initial term of the AVC, and without specific quantity to calculate exact AVC, the decision to produce is based on the expectation that the selling price exceeds the base AVC, indicating the firm should produce. The detailed calculation of exact AVC at equilibrium quantity is not provided, but the comparison suggests that as long as the selling price is above the base AVC, the firm would find it profitable to produce. This is a simplified approach to illustrate the decision-making process based on the given information.

Consider a Competitive Industry and a Price-Taking Firm That Produces Qd=10,000−10,000P+1.0MQ _ { d } = 10,000 - 10,000 P + 1.0 MQd​=10,000−10,000P+1.0M

Consider a Competitive Industry and a Price-Taking Firm That Produces $Q _ { d } = 10,000 - 10,000 P + 1.0 M$