Final Review Questions
Q1. Suppose the following information is known about a perfectly competitive industry and a typical firm in the industry:
Market Demand: Q = 6500 - 100P
Firm Total Fixed Cost: TFC = 600
Market Supply: Q 1200P
Firm Total Variable Cost: TVC = 0.005Q2
A. In one diagram, graph the market demand and supply functions (or curves). In a second diagram, graph the firm's demand, marginal revenue (MR), average revenue (AR), marginal cost (MC), and average variable cost (AVC) functions (or curves). Be certain to properly label the axes.
B. Calculate the equilibrium price (P*) and equilibrium quantity of the good produced and traded in the market (Q*). Also, calculate the consumer surplus (CS) realized in equilibrium.
C. Considering the market price determined in part 'B', calculate the output produced by a typical firm and the associated profit or loss if its objective is to maximize total profit or to minimize total operating loss.
D. Considering the market price determined in part 'B', calculate the output produced by a typical firm and the associated profit or loss if its objective is to maximize per-unit profit or to minimize per-unit operating loss.
E. Suppose that instead of being a perfectly competitive market, the market is comprised of one seller (a monopolist.). The market demand function and the firm's cost functions are the same as those described above. Calculate the level of output and the associated price if the firm's objective is to maximize total profit. Also, calculate the resulting profit and consumer surplus. Note: You might first depict the scenario graphically to assist with your calculations.
Q2. Suppose the production of a good is controlled by a single firm. The market demand for the good is characterized by the equation Q = 200 - 0.5P. The total cost of production is described by the cost function TC = 20Q.
A. Suppose the firm employs a uniform pricing strategy. 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.
D. Suppose that instead of practicing uniform pricing, that the firm is able to perfectly price discriminate. Calculate the profit maximizing level of output and profit resulting under this alternative pricing strategy.
Q3. Consider a profit maximizing monopolist. Its production function is Cobb-Douglass and of the form:
Q = 2L0.5K0.5 where Q = units of output: L = units of labor; K = units of capital
The level of capital (K) is fixed at 4 units, the price of capital (PK) is $20 per unit, and the price of labor (PL) is $8 per worker. The demand for the firm's output is represented by the (inverse) demand function P = 200 - 0.25Q.
A. Given the above information, derive the firm's total fixed cost (TFC) function, total variable cost (TVC) function, and total cost (TC) function. Be certain to show all of your steps and calculations.
B. Given the above information, derive the firm's total revenue (TR) function.
C. Construct the firm's profit function and determine the profit maximizing level of output and price. Also, calculate the resulting profit.
D. Depict the profit maximizing outcome graphically. Be certain to include the firm's demand function. marginal revenue function, marginal cost function, and average total cost function. Also, identify in your diagram the level of output, price and profit that you calculate in 'C'.
E. Suppose that instead of practicing uniform pricing, that the firm is able to perfectly price discriminate. Calculate the profit maximizing level of output and profit resulting under this alternative pricing strategy.
Q4. Consider a monopoly facing an inverse market demand function characterized by P = 160 - 0.25Q and cost function characterized by TC = 10Q.
A. Write the monopolist's profit function and calculate the profit maximizing level of output (Q*) and price (P*) and the associated profit.
B. Suppose a specific tax is imposed upon the sales of the monopolist. Specifically, a per-unit tax t = $5 must be paid on each unit sold. Write the monopolist's profit function that reflects the imposition of the tax and calculate the profit maximizing level of output and price and the associated profit.
C. Calculate the portion of the tax that is paid by the consumer on each unit.
D. Suppose instead that an ad valorem tax is imposed upon the sales of the monopolist. Specifically, an amount equal to a = $0.05 must be paid on each dollar of revenue received by the firm. Write the monopolist's profit function that reflects the imposition of the tax and calculate the profit maximizing level of output and price and the associated profit with the tax imposed.
E. Calculate the total tax revenue generated by the specific tax and the total revenue collected by ad valorem tax.