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Managers often study the profit margin-sales relation over the life cycle of individual products, rather than the more direct profit-sales relation. In addition to the economic reasons for doing so, are there statistical advantages as well? (Note: Profit margin equals profit divided by sales.)
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It is interesting to see how managers often study the profit margin-sales relation over the life cycle of individual products, rather than the more direct profit-sales relation. This is because profit margins are a good indicator of the relative profits that a firm can make from a given product. High profit margins suggest that customers value the product and still want to buy it which is good for a firm while low profit margins suggest the opposite.
Besides this there are some statistical advantages as well. For instance, profit and sales are both related to the size of a firm which may lead to a relation between the size of the firm and the variation in the disturbance term for a given profit-sales relation thereby leading to heteroscedasticity which may limit the accuracy of the required information.
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Explain how shifting demand and supply curves makes market demand estimation difficult.
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Market demand estimation is possible when all the independent variables can be identified and separated from the dependent variable. It is only then that the estimation of market demand can be done. Otherwise, one can get stuck in what is called as the identification problem. When demand and supply curves keep shifting it becomes difficult to predict their function and thereby almost impossible to estimate the market demand. This problem usually occurs because some of the factors that affect demand also affect supply which may not allow us to identify the two separately.
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Revenue Versus Profit Maximization. On weekends during summer months, Eric Cartman rents jet skis at the beach on an hourly basis. Last week, Cartman rented jet skis for 20 hours per day at a rate of $50 per hour. This week, rentals fell to 15 hours per day when Cartman raised the price to $55 per hour. Using these two price-output combinations, the relevant linear demand and marginal revenue curves can be estimated as
P = $70 - $1 Q and MR = $70 - $2 Q
A. Calculate the revenue-maximizing price-output combination. How much are these maximum revenues? If marginal cost is $30 per hour, calculate profits at this activity level, assuming TC = MC × Q.
B. Calculate the profit-maximizing price-output combination along with revenues and profits at this activity level.
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A. By setting MR=0 and solving for Q, we get the revenue maximizing price-output combination. The calculations are as follows:
Now, calculating MR:
Note that
so it is a revenue maximizing model.
Setting this equal to 0, we get the following equation:
Thus, on solving we get Q equal to 35 and further we can calculate P as follows:
Thus, P equals $35.
For this level of P and Q, TR would be the product of the two which equals $1,225 per day.
Now, profits are calculated by subtracting total cost from total revenue. The total cost is Q times the marginal cost which is $30 times 35. On calculating, we see that there is a profit of $175 per day.
B. For calculating the profit maximizing level of output, we set
or MR=MC as shown below:
On further calculation, we get Q as 20 which can be substituted in the equation for P to get P as $50.
Note that
so it is a profit maximizing model.
For this level of P and Q, TR would be the product of the two which equals $1,000 per day.
Now, profits are calculated by subtracting total cost from total revenue. The total cost is Q times the marginal cost which is $30 times 20. On calculating, we see that there is a profit of $400 per day.
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Revenue Versus Profit Maximization. The Best Buy Company, Inc., is a leading specialty retailer of consumer electronics, personal computers, entertainment software, and appliances. The company operates retail stores and commercial eb sites, the best known of which is bestbuy.com. Recently, this site offered a home theater unit with a 5-disc DVD player, MP3 playback, and digital AM/FM. At a price of $1,100, weekly sales totaled 2,500 units. After a $100 online rebate was offered, weekly sales jumped to 5,000 units. Using these two price-output combinations, the relevant linear demand and marginal revenue curves can be estimated as
P = $1 , 200 - $0. 04 Q and MR = $1 , 200 - $0. 08 Q
A. Calculate the revenue-maximizing price-output combination and revenue level. If Best Buy's marginal cost per unit is $800, calculate profits at this activity level assuming TC = MC × Q.
B. Calculate the profit-maximizing price-output combination. Also calculate revenues and
profits at the profit-maximizing activity level.
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A simple regression TR a + bQ is not able to explain 19 percent of the variation in total revenue. What is the coefficient of correlation between TR and Q?
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"When I go to the grocery store, I find centsoff coupons totally annoying. Why can't they just cut the price and do away with the clutter?" Discuss this statement and explain why coupon promotions are an effective means of promotion for grocery retailers, and popular with many consumers.
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Multiplicative Demand Functions. Getaway Tours, Inc., has estimated the following multiplicative demand function for packaged holiday tours in the East Lansing, Michigan, market, using quarterly data covering the past 4 years (16 observations):
Here, Q y is the quantity of tours sold, P y is average tour price, P x is average price for some other good, A y is tour advertising, A x is advertising of some other good, and I is per capita disposable income. The standard errors of the exponents in the preceding multiplicative demand function are
A. Is tour demand elastic with respect to price?
B. Are tours a normal good?
C. Is X a complement good or substitute good?
D. Given your answer to part C, can you explain why the demand effects of A y and A x are both positive?
Here, Q y is the quantity of tours sold, P y is average tour price, P x is average price for some other good, A y is tour advertising, A x is advertising of some other good, and I is per capita disposable income. The standard errors of the exponents in the preceding multiplicative demand function are
A. Is tour demand elastic with respect to price?
B. Are tours a normal good?
C. Is X a complement good or substitute good?
D. Given your answer to part C, can you explain why the demand effects of A y and A x are both positive? Essay
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Market Demand. Gregory House, a Philadelphia-based management consultant, has been asked to calculate and analyze market demand for a new video game that is to be marketed to retail ( R ) and wholesale ( W ) customers over the Internet.
The client estimates fixed costs of $750,000 per year for the product, and that licensing fees and other marginal costs will be $20 per unit. The client has also provided the following annual demand information:
P R = $62. 50 - $0. 0005 Q R
P w = $50 - $0. 002 Q W
A. Express quantity as a function of price for both retail and wholesale customers. Add these quantities together to calculate the market demand curve. Graph the retail, wholesale, and market demand curves for prices ranging from $65 to $35 per unit.
B. Fill in the following table:
C. Calculate the profit-maximizing price-output combination and total profit?
C. Calculate the profit-maximizing price-output combination and total profit? Essay
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In a regression-based estimate of a demand function, the beta coefficient for advertising equals 3.75 with a standard deviation of 1.25 units. What is the range within which there can be 99 percent confidence that the actual parameter for advertising can be found?
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Regression Analysis. Identify each of the following statements as true or false and explain why:
A. A parameter is a population characteristic that is estimated by a coefficient derived from a sample of data.
B. A one-tail t test is used to indicate whether the independent variables as a group explain a significant share of demand variation.
C. Given values for independent variables, the estimated demand relation can be used to derive a predicted value for demand.
D. A two-tail t test is an appropriate means for testing direction (positive or negative) of the influences of independent variables.
E. The coefficient of determination shows the share of total variation in demand that cannot be explained by the regression model.
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Multiple Regression. Colorful Tile, Inc., is a rapidly growing chain of ceramic tile outlets that caters to the do-it-yourself home remodeling market. In 2007, 33 stores were operated in small to medium-size metropolitan markets. An in-house study of sales by these outlets revealed the following (standard errors in parentheses):
Q = 4 - 5 P + 2 A + 0. 2 I + 0. 25 HF
(3) (1. 8) (0. 7) (0. 1) (0. 1)
R 2 = 93 %, Standard Error of the Estimate = 6
Here, Q is tile sales (in thousands of cases), P is tile price (per case), A is advertising expenditures (in thousands of dollars), I is disposable income per household (in thousands of dollars), and HF is household formation (in hundreds).
A. Fully evaluate and interpret these empirical results on an overall basis using
statistic and SEE information.
B. Is quantity demanded sensitive to "own" price?
C. Austin, Texas, was a typical market covered by this analysis. During 2007 in the Austin market, price was $5, advertising was $30,000, income was an average $55,000 per household, and the number of household formations was 4,000. Calculate and interpret the relevant advertising point elasticity.
D. Assume that the preceding model and data are relevant for the coming period. Estimate the probability that the Austin store will make a profit during 2008 if total costs are projected to be $300,000.
statistic and SEE information.
B. Is quantity demanded sensitive to "own" price?
C. Austin, Texas, was a typical market covered by this analysis. During 2007 in the Austin market, price was $5, advertising was $30,000, income was an average $55,000 per household, and the number of household formations was 4,000. Calculate and interpret the relevant advertising point elasticity.
D. Assume that the preceding model and data are relevant for the coming period. Estimate the probability that the Austin store will make a profit during 2008 if total costs are projected to be $300,000. Essay
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"Demand for higher education is highest among the wealthy. This has led to an upward-sloping demand curve for college education. The higher the tuition charged, the greater is demand." Discuss this statement.
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Demand Estimation Concepts. Identify each of the following statements as true or false and explain why.
A. The effect of a $1 change in price is constant, but the elasticity of demand will vary along a linear demand curve.
B. In practice, price and quantity tend to be individually rather than simultaneously determined.
C. A demand curve is revealed if prices fall while supply conditions are held constant.
D. The effect of a $1 change in price will vary, but the elasticity of demand is constant along a log-linear demand curve.
E. Consumer interviews are a useful means for incorporating subjective information into demand estimation.
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Linear Demand Curve Estimation. Xerox Corporation develops, manufactures, and services document equipment and software solutions worldwide. Assume the company offered $75 off the $1,475 regular price on the Phaser 6360, a durable high-speed color copier, and Internet sales jumped from 700 units to 800 units per week (see http://www.office.xerox.com).
A. Estimate the color copier demand curve, assuming that it is linear.
B. If marginal costs per unit are $650, calculate the profit-maximizing price-output combination. [Remember: The marginal revenue curve has the same intercept as the demand curve, but has twice its negative slope (falls twice as fast).]
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Linear Demand Curve Estimation. Kenny McCormick manages a 100-unit apartment building and knows from experience that all units will be occupied if rent is $900 per month. McCormick also knows that, on average, one additional unit will go unoccupied for each $10 increase in the monthly rental rate.
A. Estimate the apartment rental demand curve assuming that it is linear and that price is expressed as a function of output.
B. Calculate the revenue-maximizing apartment rental rate. How much are these maximum revenues?
C. If all costs are fixed, what is the profit-maximizing number of vacant apartments? Explain your answer.
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If a regression model estimate of total profit is $50,000 with a standard error of the estimate of $25,000, what is the chance of an actual loss?
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How do linear and log-linear models differ in terms of their assumptions about the nature of demand elasticities?
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"Rapid innovation in the development, assembly, and delivery of personal computers has led to a sharply downward-sloping market demand curve for Dell, Inc." Discuss this statement.
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