1. A sporting goods company has hired a management consulting firm to analyze demand in 20 regional markets for one of its major products: a treadmill. The consultant uses data to estimate the following equation:
Where Q = Number of treadmills demanded
P = $1,200; Price of treadmills
A = $200; Advertising expenditures (in thousands)
I = $60; GDP per capita (in thousands)
PX = $1,000; Competitor’s price
= $150; Competitor’s advertising expenditures (in thousands)
a. Calculate the amount demanded for this product using the information given above
b. Plot the demand curve with P on the vertical axis and Q on the horizontal axis.
c. Calculate the price to sell 2,000 units.
d. What would be the effect on the sales of treadmills if the competitor reduces price by $100? What should be the change in P to offset the decrease in PX?
e. In response to competitor’s strategy of reducing PX, what else can the company do to keep sales at the same level if does not want to change P? (Base your answer on the information given above.)
2. The XYZ Tech Store had been selling a spreadsheet program at a rate of 100 units per month and a graphics program at a rate of 50 units per month. In September 2012, the EXZ Tech Store’s supplier lowered the price for the spreadsheet program, and the XYZ Tech Store lowered its price from $400 to $350.
a. If the price elasticity is -2.14, how many spreadsheets will be sold?
b. If the cross elasticity of spreadsheets and graphics program is -1.11, how many graphics programs will be sold if the initial quantity sold were 50?
c. As a result of this change in spreadsheet price what will happen to total revenue? Why? (No numerical answer needed. Just an explanation)
3. One of the leading dishwasher producers has estimated the following demand equation after analyzing 35 regional markets:
Q = + 20,000 – 40P + 30A + 20 - 40 + 90 I
(12000) (18.2) (44) (8.5) (52) (42)
R2 = 0.82 F = 32.26
The variables and their assumed values are
Q = Quantity
P = Price of basic model = 400
A =Advertising expenditures = 50
=Average price of the competitor’s product = 500
= competitor’s advertising expenditures = 30
I = per capita income = 50
a. Compute the elasticities for each variable. On this basis, discuss the relative impact that each variable has on the demand. What implications do these results have for the firm’s marketing, pricing, and production policies?
b What would be the effect of a 6 unit increase in the competitor’s advertising expenditures?
c. What would be the change in your advertising expenditures to offset your competitor’s strategy?
d. Conduct a t-test for the statistical significance of each variable. Discuss the results of the t-tests in light of the policy implications mentioned.
e. What proportion of the variation in sales is explained by by the independent variables in the equation? How confident are you about this answer? Explain using the F-test.
4. Given the Production Function: Q = 30L + 9L2 -0.5 L3, where Q = Output and L = labor input
a. At what value of L will Diminishing Returns take effect?
b. Calculate the range of values for labor over which stages I, II, and III occur?
c. Suppose that the wage rate is $24 and the price of output is $2 per unit. How many workers should
the firm hire?
d. At what value of L will Q be at its maximum? What is the maximum amount of Q?
e. If demand estimate for Q is between 1600 and 2000, what would be your plan in the long run to meet
customer demand?
5. Given the cost function: ,
a. At what level of Q does the firm achieve minimum average cost?
b. Assume that this is a firm in a perfectly competitive industry and the competitive price is $2/unit.
What should the firm do in the long-run?