Consider the following model of supply and demand. P = 6 – 3Q P = 1 + 2Q (a) Identify the demand function and describe it in terms of gradient and intercept. (b) Using algebra find the single combination of P and Q that satisfies both of these equations and interpret in economic terms. (c) Roughly sketch these two functions on the same graph. (d) Show the values of P and Q where the functions cross the axes and clearly label the point of intersection.
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- in excel Price Demand 2000 4500 2800 3600 3500 1850 4000 1200 5000 820 Based on the data above estimate the demand function. When you estimate demand curve, please compare the following options and choose the one with highest R square Exponential Linear PowerA company estimated that the relationship between the unit price and demand per month for a potential new product is approximated by P = $ 100 – $ 0.1D. The company can produce the product by increasing fixed costs $ 17,500 per month, and the estimated variable costs is $ 40 per unit. What is the optimal demand, D*, and based on this demand, should the company produce new product? Why? a) Work out the complete solution by differential calculus, starting with formula for profit or loss per month b) Solve graphically for an approximate answer(Marginal Analysis). A retailer has determined that the monthly sales of a watch are 150 units when the price is $50, but decrease to 120 units when the price is $60. Assume that the demand is a linear function of the price. (4a) Find the demand as a linear function of the price (4b) Find the revenue R as a function of x (4c) Approximate the change in revenue for a one-unit increase in sales when x = 141
- The profit,P,of a company that manufactures and sells N units of a certain product is modeled by the function P(N)=R(N)-C(N) The revenue function,R(N)=S·N, is the selling price S per unit times the number N of units sold. The company's cost,C(N)= Co +Cop(N), is a sum of two terms. The first is a constant Co describing the initial investment needed to set up production. The other term, Cop(N), varies depending on how many units the company produces, and represents the operating costs. Companies care not only about profit, but also marginal profit, the rate of change of profit with respect to N. Assume that S=$50,Co=$75,000, Cop(N)=$50✓N,and that the company currently sells N= 100 units. Compute the marginal profit at this rate of production.Round your answer to one decimal place.The multivariate demand function below will be needed for questions 12-18. Setting: Grapple, Inc. is a leading seller of laptop personal computers. However, they want to become a leading tablet seller, too. Your marketing department, aided by your economics staff, has estimated a function to help you in the quest for market leader in tablets. The variables are defined after the function. Qg = 10000 - 25Pg + 20Ph + 30Pr - 15dv - 35Psc - 10Pmm + 0.05Ag + 0.03A -25C + 0.1Y Qg = the number of Grapple tablet computers demanded per week. Pg = the price of each new Grapple tablet (in $). Ph = the price of each Hewpaq tablet (in $). Pr = the price of each Ronova tablet. Pdv = the price to equip a tablet with Holographic digital video (in $, this is an upgrade option that enables three-dimensional graphics on a tablet. Two-dimensional graphics is standard equipment). Psc = the price of various screen sizes (in $, a 8 inch is standard, but upgrade options are 10…Q2 The manufacturer of a low-sugar bottled juice estimated the following demand equation for its product using data from 25 retail stores around Dover city for the month of November: Q=-2000-15 Pje+ 8.4Px + 0.51 + 0.4A (220) (5.0) (5.6) (0.2) (0.16) R²=0.57 n=25 F = 6.83 Assume the following values for the independent variables: Standard error 1 Q denotes quantity sold per month Pje (denotes price of the bottled juice) = 240 (in cents) P. (denotes price of leading competitor's product) - 300 (in cents) I (denotes per capita income of the standard residential district in which the retail store is located) = 4000 (in dollars) A (denotes monthly advertising expenditure) = 7700 (in dollars) Using this information, answer the following questions: a. Compute elasticities for each variable.. b. Do you think that this firm should cut its price to increase its market share?
- Q2 The manufacturer of a low-sugar bottled juice estimated the following demand equation for its product using data from 25 retail stores around Dover city for the month of November: Q=-2000-15 Pje+ 8.4Px + 0.51 + 0.4A (220) (5.0) (5.6) (0.2) (0.16) R²=0.57 n=25 F = 6.83 Assume the following values for the independent variables: Standard error 1 Q denotes quantity sold per month Pje (denotes price of the bottled juice) = 240 (in cents) P. (denotes price of leading competitor's product) - 300 (in cents) I (denotes per capita income of the standard residential district in which the retail store is located) = 4000 (in dollars) A (denotes monthly advertising expenditure) = 7700 (in dollars) Using this information, answer the following questions: a. Compute elasticities for each variable.. b. Do you think that this firm should cut its price to increase its market share? Explain..ATV is a price-setting firm and estimates the demand for its cement using a demand function in the linear form: Q = f( P, M, PR) where Qc = demand for cement/month (in yards) Pc = the price of cement per yard, M = country’s tax revenues per capita, and PR = the price of asphalt per yard. DEPENDENT VARIABLE Qc R- SQUARE P- VALUE ON F 64 0.8093 0.0001 INDEPENDENTVARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 8.20 4.01 2.04 0.0461 PC -3.54 1.64 -2.16 0.0357 M 0.64287 0.19 3.38 0.0014 PA 0.7854 0.38 2.07 0.0439 10. Write the resulting regression equation.1) In a relationship among total, average and marginal products, where TP is maximized: * A)AP is maximized B)AP is equal to zero C)MP is equal to zero D)MP is maximized Q2) The method which can give some information in estimating demand of a product that hasn’t yet come to market is: * a)a statistical demand analysis B)the consumer survey C)market experimentation D)plotting the data 3) An example of a time series data set is one for which the: * 1)data would be collected for a given firm for several consecutive periods (e.g., months). 2)data is created from a random number generation program. 3)data would be collected for several different firms at a single point in time. 4)regression analysis comes from data randomly taken…
- A firm believes a product’s sales volume (S) depends on its unit selling price (P) as S = $100 − P. The production cost (C) is $1000 + 10S. (a) Graph the sales volume (S) from 0 to 100 on the x axis, total cost and total income from $0 to $2500 on the y axis, C = $1000 + 10S, and plot the curve of total income. Mark the breakeven points on the graph. (b) Determine the breakeven point (lowest sales volume at which total sales income just equals total production cost). (c) Determine the sales volume (S) at which the firm’s profit is a maximum.DEPENDENT VARIABLE Qc R- SQUARE P- VALUE ON F 64 0.8093 0.0001 INDEPENDENTVARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 8.20 4.01 2.04 0.0461 PC -3.54 1.64 -2.16 0.0357 M 0.64287 0.19 3.38 0.0014 PA 0.7854 0.38 2.07 0.0439 7. If the price of asphalt (PR) decreases by 15, what will happen to the estimated quantity of cement demanded? Q = f( P, M, PR) where Qc = demand for cement/month (in yards) Pc = the price of cement per yard, M = country’s tax revenues per capita, and PR = the price of asphalt per yard.A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result, only 40 units were sold in a week. The manufacturers fixed costs of production are $1,710 a week and variable costs are $9 per unit. You are required to: d. Assuming a sudden change in trading conditions resulting in a 20% reduction in demand at all price levels, to find the equation of the new demand function and to recommend how the manufacturer should respond.