1. In a competitive industry, the short-run average variable cost (AVC) of a firm is:AVC = 600 20Q 0.5Q2a. Derive the firms short-run supply equationb. Determine the minimum possible price (shut-down price) for the firm.Hint: Competitive firms short-run supply curve is its MC curve. MC is the derivative of VC.2. A small tractor producing firms total cost and demand equations are as followsC = 37,500,000 + 5,000Q + 1.5Q2P = 30,000 Qa. Find optimal output and price and its profit.b. Because of an increased foreign competition, the demand falls permanently to:P = 20,000 QThe firm is considering closing its plan immediately. By doing so, it can save $18 million of itsannual$37.5 million in fixed costs. Alternatively, it can continue to operate the plant for 12 months afterwhich if it shuts down it can walk away from its labor contracts and lease payments and incur nocontinuing costs. Determine its most profitable or least-cost operating strategy.