Multiple Regression 2023 Business Finance
2023 Homework Problems 1 Multiple Regression Hawkeye Pierce Inc finds in a simple regression analysis that demand increases with
1. Multiple Regression. Hawkeye Pierce, Inc., finds in a simple regression analysis that demand
increases with an increase in advertising, and falls as advertising expenditures are reduced.
Similarly, a simple regression analysis of product demand and price reveals that demand
increases with a decrease in average price, and falls as prices are raised. Coefficient estimates for
each independent variable are statistically significant, as is the level of overall explanation
achieved, as revealed by the coefficient of determination (R2). However, when both advertising
and price are included as independent variables in a multiple regression model, neither variable
has a statistically significant coefficient estimate.
Explain the difference between coefficient estimates obtained using a simple
regression model versus a multiple regression model.
What is the source of the difficulty encountered here in measuring the marginal
influences of advertising and price on demand? Any suggestions?
2. Quantity Demanded. The Sharper Edge, Inc. is a leading retailer of Yingsu Knives, a set of
kitchen cutlery, which it markets on a nationwide basis. SEI knife sets are either sold directly to
the public through national television marketing programs, or given away as promotional items.
Operating experience during the past year suggests the following demand function for its knife
Q = 4,000 − 4,000P + 10,000N + 0.25I + 0.4A
Where Q is quantity, P is the price ($), N is the average Nielson rating of television programs
during which SEI advertises Yingsu Knives, I is average disposable income per household ($),
and A is advertising expenditures ($).
Determine the demand curve faced by SEI in a typical market where P = $35, N
= 18.5, I = $44,000, and A = $500,000. Show the demand curve with quantity
expressed as a function of price, and price expressed as a function of quantity.
Calculate the quantity demanded at prices of $40, $35, and $30.
Calculate the prices necessary to sell 264,000, 292,000, and 320,000 sets of
3. Income Elasticity. The Electronics Warehouse, Inc. is a leading retailer of home theater systems.
Demand for home theater systems is sensitive to changes in national income. Electronics
retailing is highly competitive, so retail demand for home theater systems is also very pricesensitive. During the past year, the Electronics Warehouse sold 550,000 home theater systems at
an average retail price of $4,000 per unit. This year, GDP per household is expected to fall from
$58,800 to $53,200 as the nation enters a steep recession. Without any price change, the
Electronics Warehouse expects current-year sales to fall to 450,000 units.
Calculate the implied arc income elasticity of demand.
Given the projected fall in income, the sales manager believes that current
volume of 550,000 units could only be maintained with a price cut of $500 per
unit. On this basis, calculate the implied arc price elasticity of demand.
Holding all else equal, would a further increase in price result in higher or lower
4. Short-run Firm Supply. Produce Pride, Inc., supplies sweet corn to canneries located
throughout the Missouri River Valley. Like many grain and commodity markets, the market for
sweet corn is perfectly competitive. With $500,000 in fixed costs, the company’s total and
marginal costs per ton (Q) are:
TC = $500,000 + $400Q + $0.04Q2
MC = ∆ TC/∆ Q = $400 + $0.08Q
Calculate the industry price necessary to induce short-run firm supply of 5,000,
10,000, and 15,000 tons of sweet corn. Assume that MC > AVC at every point
along the firm’s marginal cost curve and that total costs include a normal profit.
Calculate short-run firm supply at industry prices of $400, $1,000, and $2,000
5. Short-run Firm Supply. Nature’s Best, Inc., supplies asparagus to canners located throughout
the Mississippi River valley. Like several grain and commodity markets, the market for
asparagus is perfectly competitive. Marginal cost per ton of asparagus is:
MC = $1.50 + $0.0005Q
Calculate the industry price necessary for the firm to supply 500, 1,000, and
Calculate the quantity supplied by Nature’s Best at industry prices of $1.50,
$2.25, and $2.75 per pound.
6. Competitive Strategy. Bob Ice owns and operates Bob’s Music Center, Ltd., a small firm that
offers music lessons in Huntsville, Alabama. Given the large number of competitors and the lack
of entry barriers, it is reasonable to assume that the market for music lessons is perfectly
competitive and that the average $60 per hour price equals marginal revenue, P = MR = $60.
Assume that Bob’s annual operating expenses are typical of several such firms and individuals
operating in the local market, and can be expressed by the following total and marginal cost
TC = $100,000 + $10Q + $0.005Q2
MC = $10 + $0.01Q
where TC is total cost per year, MC is marginal cost, and Q is the number lessons given. Total
costs include a normal profit and allow for Bob’s employment opportunity costs.
Calculate Bob’s profit-maximizing output level.
Calculate Bob’s economic profits at this activity level. Is this activity level
sustainable in the long run?
7. Market Structure Concepts. Indicate whether each of the following statements is true or
false and explain why.
A. Equilibrium in monopolistically competitive markets requires that firms be
operating at the minimum point on the long-run average cost curve.
B. A high ratio of distribution cost to total cost tends to increase competition by
widening the geographic area over which any individual producer can
C. The price elasticity of demand tends to fall as new competitors introduce
D. An efficiently functioning cartel achieves a monopoly price/output
E. An increase in product differentiation tends to increase the slope of firm
8. Monopolistically Competitive Demand. Would the following factors increase or decrease the
ability of domestic auto manufacturers to raise prices and profit margins? Why?
A. Decreased import quotas
B. Elimination of uniform emission standards
C. Increased automobile price advertising
D. Increased import tariffs (taxes)
E. A rising value of the dollar, which has the effect of lowering import car prices
9. Monopoly Concepts. Indicate whether each of the following statements is true or false, and
A. The Justice Department generally concerns itself with significant or flagrant
offenses under the Sherman Act, as well as with mergers for monopoly covered
by Section 7 of the Clayton Act.
B. When a single seller is confronted in a market by many small buyers,
monopsony power enables the buyers to obtain lower prices than those that
would prevail in a competitive market.
C. A natural monopoly results when the profit-maximizing output level occurs at a
point where long-run average costs are declining.
D. Downward-sloping industry demand curves characterize both perfectly
competitive and monopoly markets.
E. A decrease in the price elasticity of demand would follow an increase in
Explain how GDP (Gross Domestic Product) is calculated based on Fiscal Policy from
John Maynard Keynes and the Keynesian economics equation: Y = C + I + G – (X – M).
11. Explain the Marginal Propensity to Consume (MPC), the Marginal Propensity to Save
(MPS), and how to calculate the multiplier. Explain how the economic multiplier works.
12. What is M1 and M2? Why are they important to Monetary Policy?
13. How is the change in money supply calculated with the money mulitiplier?
14. What are the three monetary policy options that the Federal Reserve can use
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