Questions -
Question 1 - Consider a perfectly competitive firm operating in the short-run, Market demand and market supply are such that the equilibrium trading price is P = $6 per unit. The firm's total fixed costs are $100, and its total variable costs are characterized by the function TVC = 2Q + 0.002Q2.
A. Derive the firm's total revenue (TR) function, average revenue (AR) function, marginal revenue (MR) function, marginal cost (MC) function, as average variable cost (AVC) function, and average total cost (ATC) function.
B. In one diagram, graph the TR and TC functions and identify the level of output that maximizes total profit and the resulting maximum total profit. In a second diagram immediately below the first diagram, graph the demand, AR, MR, MC, and ATC functions and identify the level of output that maximizes total profit and the resulting maximum total profit. Be certain to properly label the axes and identify the vertical and horizontal intercepts.
C. Construct the firm's profit function. From this, calculate the level of output that maximize total profit, and calculate the resulting maximum profit. Show all steps for credit.
Question 2 - Suppose the market for a good is controlled by a single firm. The market demand for the good is characterized by the function Q = 250 - 2P, and the firm's total cost function TC = 10Q.
A. Derive the firm's total revenue (TR) function, average revenue (AR) function, marginal revenue (MR) function, marginal cost (MC) function, and average total cost (ATC) function.
B. In one diagram, graph the TR and TC functions and identify the level of output that maximizes total profit and the resulting maximum total profit. In a second diagram immediately below the first diagram, graph the demand, AR, MR, MC, and ATC functions and identify the level of output that maximizes total profit and the resulting maximum total profit. Be certain to properly label the axes and identify the vertical and horizontal intercepts.
C. Construct the firm's profit function. From this, calculate the level of output that maximizes total profit. Also, calculate the profit maximizing price and the maximum profit. Also, calculate the price elasticity of demand at the level of output that maximizes total profit. Show all steps for credit.