Question

Question 3: Textbook

• Product: Textbook
• Selling price: $60
• Sales in January: 500
• Price elasticity: 5

The information above is provided by a bookstore. The store manager wants to determine if $50 is the profit maximization price for this textbook. He also provides the following information:

• Purchase price from publisher: $40

Question 3.1: Please create a linear demand curve based on the given information.

[Please type the equation of the linear demand curve]

Question 3.2: Use Excel Solver to find out the profit maximizing price of this textbook.

Answer 1

3.1)

• A linear demand curve is the graphical representation of the relationship between the price of a good and the quantity of that good consumers are willing to pay at a certain price at a point in time.
• The slope,or rate that the line rises or falls, is equal to the difference between two quantities of a product-usually represented on the horizontalaxis on the graph--dividedby the difference price of two points of the graph --usually on the vertical axis.
• Linear curves rarely exist in the real world because demand depends in large part on elasticity of demand,or how consumers react to a change in price.
• Also the realtionship between demand and price is not always constant.Some products are in demand reagardless of price .
• for instance ,costumaors probably use about the same amount of electricity regardless of price because it is essential to living .
• on the other hand ,televisions are a luxary , so consumers useually become exponentially more willing to buy a unit as the price drop .
• upply Curve
• Using a demand curve can help you determine exactly how much product to produce or the best price for it so you maximize your profit..
• To find the optimal price point -- where the demand for a good meets supply -- you must include a supply curve. A supply curve uses the same slope formula as the demand curve but is graphed as the opposite of the demand curve.
• Look at data from your past sales to graph a demand curve. You may want to hire a market research firm to help you set the price on your goods or calculate production level if you do not have sales data.
• You may also need to use your own estimation skills and to factor in the economic environment.
• For instance, Christmas decorations and new toys usually spike in price right before the holidays but fall during the beginning of the year because demand plummets. In the world of supply and demand, price increases as demand increases, and vice versa.
• 3.2)

• In economics, profit maximization is the short run or long run process by which a firm may determine the price, input, and output levels that lead to the highest profit.

• Neoclassical economics, currently the mainstream approach to microeconomics, usually models the firm as maximizing profit.

• There are several perspectives one can take on this problem. First, since profit equals revenue minus cost, one can plot graphically each of the variables revenue and cost as functions of the level of output and find the output level that maximizes the difference (or this can be done with a table of values instead of a graph).

• Second, if specific functional forms are known for revenue and cost in terms of output, one can use calculus to maximize profit with respect to the output level.

• Third, since the first order condition for the optimization equates marginal revenue and marginal cost, if marginal revenue (mr) and marginal cost(mc) functions in terms of output are directly available one can equate these, using either equations or a graph.

• Fourth, rather than a function giving the cost of producing each potential output level, the firm may have input cost functions giving the cost of acquiring any amount of each input, along with a production function showing how much output results from using any combination of input quantities.

• In this case one can use calculus to maximize profit with respect to input usage levels, subject to the input cost functions and the production function. The first order condition for each input equates the marginal revenue product of the input (the increment to revenue from selling the product caused by an increment to the amount of the input used) to the marginal cost of the input.

• For a firm in a perfectly competitive market for its output, the revenue function will simply equal the market price times the quantity produced and sold, whereas for a monopolist, which chooses its level of output simultaneously with its selling price, the revenue function takes into account the fact that higher levels of output require a lower price in order to be sold.

• An analogous feature holds for the input markets: in a perfectly competitive input market the firm's cost of the input is simply the amount purchased for use in production times the market-determined unit input cost, whereas a monopsonist’s input price per unit is higher for higher amounts of the input purchased.

• The principal difference between short-run and long-run profit maximization is that in the long run the quantities of all inputs, including physical capital, are choice variables, while in the short run the amount of capital is predetermined by past investment decisions. In either case there are inputs of labor and raw materials.

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