For A Linear Inverse Demand Function, Increase In Output Wil
For A Linear Inverse Demand Function Increases In Output Will Ca
For a linear (inverse) demand function, increases in output will cause total revenue to decrease when marginal revenue is a. Positive b. Negative c. Unit elastic d. Elastic
Suppose the production function is given by Q = 10K + 4L. What is the marginal product when 5 units of capital and 10 units of labor are employed? a. 10 b. 4 c. 18 d. 9
The higher the interest rate a. The greater the present value of a future amount b. The smaller the present value of a future amount c. The greater the level of inflation d. None of the statements associated with this question are correct
The demand for good X has been estimated by Qxd = 20 - 5Px + 4Py. Suppose that good x sells at $3 per unit and good y sells for $2. Calculate the own price elasticity a. -1.15 b. -21.67 c. -5.0 d. 0
The own price elasticity of demand for apples is -1.5. If the price of apples increases by 10 percent, what will happen to the quantity of apples demanded? a. It will increase 15 percent b. It will fall 15 percent c. It will increase 10 percent d. It will fall 10 percent
Which of the following signals to firm owners that scarce resources might be better allocated to a different industry? a. Fewer government regulations in that other industry b. Profits in that other industry c. Better availability of labor in that other industry d. Cheaper cost of capital in that other industry
Other things held constant, consumer surplus decreases as: a. The price of a good decreases b. The price of a good increases c. The supply curve shifts to the right d. None of the above
Other things held constant, producer surplus increases as: a. The price of a good decreases b. The price of a good increases c. The demand curve shifts downward d. None of the above
Other things equal, the lower the interest rate: a. The lower the NPV b. The higher the NPV c. The higher the PV d. None of the statements associated with this question are correct
An excise tax of $2.00 per pound of sugar placed on the suppliers of sugar would shift the supply curve: a. Down by $2.00 b. Down by more than $2.00 c. Up by $2.00 d. Up by less than $2.00
The demand for good X has been estimated to be in Qxd = 100 - 5 in Px + 2 in Py + 4 in M. The cross-price elasticity of demand between goods X and Y is: a. 2 b. -5 c. -2 d. There is insufficient information needed to find the elasticity of good X
When the long run average cost curve is decreasing (assuming a U-shaped curve) there exist a. Economies of scale b. Diseconomies of scale c. Constant returns to scale d. None of these
A price ceiling is a. The minimum legal price that a firm can charge b. The maximum legal price that a firm can charge c. Above the competitive equilibrium price d. Equal to the competitive equilibrium price
What is the marginal net benefit of producing the fourth unit? No. Units Produced Total Revenue Total Cost a. 10 b. 7 c. 30 d.
The main reason firms may exit a market is because of a. The lack of economic profits b. Decreased technology c. Expensive labor d. High capital costs
Suppose the marginal product of capital is 16 and the marginal product of labor is 3. If the price of capital is $4 and the wage rate is $3, then in order to minimize costs the firm should use: a. More capital and less labor b. More labor and less capital c. Three times more capital than labor d. None of the answers are correct
$100 received at the end of seven years in worth how much today if the interest rate is 8 percent? a. 100/(0.08)7 b. 100/(1 + 0.08)7 c. 100/(1 + 8)7 d.
If good A is a normal good, an increase in income leads to: a. An increase in the demand for good B b. A decrease in the demand for good A c. An increase in the demand for good A d. No change in the quantity demanded for good A
When demand is unit elastic, marginal revenue will be: a. Positive b. Negative c. Zero d. There is not sufficient information to determine the marginal revenue
The difference between total costs and variable costs is: a. Marginal costs b. Average fixed cost c. Fixed cost d. None of the statements is correct
The demand curve for a good is vertical when it is: a. A perfectly inelastic good b. A unitary elastic good c. A perfectly elastic good d. An inferior good
Good X is an inferior good and its demand is given by Qxd = a0 + axPx + ayPy + amM + aHH. Then we know that: a. ax0 c. am
When the government imposes a price ceiling above the market price, the result will be that: a. Surpluses occur b. Shortages become a problem c. Supply and demand will shift up to the new equilibrium d. A price floor set above the equilibrium price will have no effect on the market equilibrium
Larger firms produce a product at larger average cost than small firms when: a. Economies of scope exist b. Diseconomies of scale exist c. Economies of scale exist d. Cost complementarities exist
When the marginal cost of producing one output is reduced when the output of another product is increased this is called: a. Cost complementarities b. Economies of scope c. Economies of scale d. The marginal rate of technical substitution
If Starbucks’s marketing department estimates the income elasticity of demand for its coffee to be 1.7, how will the prospect of an economic boom (expected to increase consumers’ incomes by 4 percent over the next year) impact the quantity of coffee Starbucks expects to sell? Answer: It will change by ____________ percent
Suppose the cross price elasticity of demand between goods X and Y is 4. How much would the price of good Y have to change in order to change the consumption of good X by 40 percent? Answer: ____________ percent
What is the value of a preferred stock that pays a perpetual dividend of $150 at the end of each year when the interest rate is 3 percent? Answer: $_________________ (round response to the nearest dollar)
A firm produces output according to a production function: Q = F(K,L) = min {2K, 2L} a. How much output is produced when K = 2 and L = 3? Answer: ______________ b. If the wage rate is $40 per hour and the rental rate on capital is $20 per hour, what is the cost minimizing input mix for producing 4 units of output? Answer: Capital __________ Labor ___________ c. How does your answer to part b change if the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour? 1. Capital and labor increase 2. It does not change 3. Capital decreases and labor increases 4. Capital increases and labor decreases
The head of the accounting department at a major software manufacturer has asked you to put together a pro forma statement of the company’s value under several possible growth scenarios and the assumption that the company’s many divisions will remain a single entity forever. The manager is concerned that, despite the fact that the firm’s competitors are comparatively small, collectively their annual revenue growth has exceeded 50 percent over each of the last five years. She has requested that the value projections be based on the firm’s current profits of $2.4 billion (which have yet to be paid out to stockholders) and the average interest rate over the past 20 years (7 percent) in each of the following profit growth scenarios. a. Profits grow at an annual rate of 10 percent _____________________ b. Profits grow at an annual rate of 5 percent _____billion(round to 2 decimal places) c. Profits grow at an annual rate of 0 percent ____billion(round to 2 decimal places) d. Profits decline at an annual rate of 3 percent ____billion(round to 2 decimal places)
Paper For Above instruction
The given set of questions covers a broad range of fundamental concepts in microeconomics and managerial economics, requiring analysis and understanding of demand functions, production functions, cost analysis, elasticity measures, market structures, and financial valuation techniques. This paper aims to systematically address each question, providing clear explanations supported by economic theory, mathematical calculations where applicable, and real-world examples to enhance comprehension.
Impact of Output on Revenue in Linear Demand
For a linear inverse demand function, the relationship between total revenue and output depends critically on the marginal revenue (MR). When output increases, total revenue initially increases if demand is elastic but decreases once demand becomes inelastic. Specifically, total revenue decreases when the marginal revenue is negative. According to economic theory, with linear demand, MR is given by a linear function with twice the slope of demand (Coulson & Rizzo, 2017). When MR is negative, further increases in output result in declining total revenue, highlighting a negative elasticity scenario.
Marginal Product of Capital
Given the production function Q = 10K + 4L, the marginal product of capital (MPK) is derived as the partial derivative of Q with respect to K, which is 10. At employed inputs of K=5 and L=10, the MPK remains constant at 10 because the production function is linear. This illustrates that increasing capital from 5 to 6 units adds 10 units of output, assuming other inputs are held constant, showcasing perfect substitutability in this context (Varian, 2014).
Interest Rate and Present Value
The interest rate directly influences the present value (PV) of future cash flows. A higher interest rate reduces PV because future sums are discounted more heavily. Conversely, a lower interest rate increases PV, making future cash flows more valuable today. This principle is foundational in finance, dictating how investors value long-term investments (Brealey, Myers, & Allen, 2020).
Price Elasticity and Demand Calculations
The own price elasticity of demand measures the responsiveness of quantity demanded to price changes. Given the demand function Qx = 20 - 5Px + 4Py and prices Px = $3, Py = $2, the elasticity is computed using the formula: Elasticity = (dQ/dPx) * (Px/Q). The derivative dQ/dPx = -5. Plugging in the numbers gives an elasticity of approximately -1.15, indicating that demand is somewhat elastic (Hirsch, 2018).
Effect of Price Changes on Quantity Demanded
Given the elasticity of -1.5 for apples, a 10% increase in price decreases the quantity demanded by 15%. This aligns with the definition of price elasticity, which states demand falls proportionally to price increases in elastic demand scenarios (Mankiw, 2014).
Market Signals and Resource Allocation
Firms interpret signals such as profits, technological advancements, and input availability as indicators that resources could be better allocated if profits rise elsewhere or costs decrease, prompting potential shifts in production. Increased profits in other industries or better labor availability signal profitability opportunities which might direct firms to new sectors (Samuelson & Nordhaus, 2010).
Consumer and Producer Surplus Dynamics
Consumer surplus diminishes when the price of a good increases, as consumers are willing to pay less than the new higher price, reducing the total benefit. Conversely, producer surplus increases as higher prices boost profit margins, ceteris paribus. Changes in supply and demand curves also influence these surpluses, reflecting market welfare shifts (Varian, 2014).
Interest Rate Effects on Net Present Value and Price Controls
Lower interest rates increase the present value (PV) of future cash flows due to reduced discounting, thus raising NPV. Price ceilings below equilibrium cause shortages, while floors above can result in surpluses, demonstrating government intervention impacts on markets (Bishop & Walker, 2019).
Elasticities in Demand and Cross-Price Relationships
The cross-price elasticity between goods X and Y, given by the formula: (dQx/dPy) (Py/Qx), is calculated from the demand function. For a demand function Qx = 100 - 5Px + 2Py + 4M, the elasticity with respect to Py is 4 (Py/Qx). With specific prices, the elasticity is 2, indicating substitute or complementary relationships based on sign and magnitude.
Cost Structures and Economies of Scale
Decreasing long-run average costs reflect economies of scale, where large outputs are produced more efficiently. A U-shaped LRAC curve signifies initial economies and eventual diseconomies as scale increases (Perloff, 2016).
Price Controls and Market Equilibrium
Price ceilings cap prices below equilibrium, causing shortages and rent-seeking behaviors. Price floors set above equilibrium can lead to surpluses if the market price cannot fall to clearing levels. These interventions distort market equilibrium and resource allocation (Parkin, 2018).
Marginal Benefits and Cost Minimization
The marginal net benefit of producing an additional unit is computed as the difference between marginal revenue and marginal cost. Efficient production occurs where marginal cost equals marginal revenue or where marginal net benefit is maximized, ensuring optimal resource utilization.
Market Entry and Exit
High costs, technological barriers, and unprofitable operations typically motivate firms to exit markets. Firms seek to maximize profits; sustained losses incentivize exit, especially when competition erodes profitability (Tirole, 2017).
Optimal Input Usage
Given marginal products and input prices, firms minimize costs by equating the marginal rate of technical substitution to the ratio of input prices. If MPK = 16 and MPL = 3, with prices $4 and $3, the optimal input mix balances these ratios, which suggests more capital usage when the ratio favors it. Changes in wages affect this balance, often leading to increased capital usage if wages decrease (Varian, 2014).
Time Value of Money
Valuing future sums involves discounting at the interest rate. The present value of $100 received in 7 years at 8% interest is computed as 100 / (1 + 0.08)^7, demonstrating the time value of money principles central to finance theory (Brealey et al., 2020).
Income and Demand for Normal Goods
An increase in income raises demand for normal goods, including those that are income-normal in nature. For example, as income increases, consumers tend to buy more of such goods, reflecting positive income elasticity (Hirsch, 2018).
Elasticity and Revenue Relationship
When demand is unit elastic, marginal revenue is zero because total revenue remains constant despite small quantity changes. Elasticity equal to -1 indicates this specific condition where changes in price do not change total revenue (Mankiw, 2014).
Cost Components
The difference between total costs and variable costs is fixed costs, which do not vary with output in the short run. Understanding fixed versus variable costs is critical in managerial decision-making and cost control (Perloff, 2016).
Demand Elasticity and Curve Shape
A vertical demand curve indicates perfectly inelastic demand, where quantity demanded does not respond to price changes. This feature is typical of necessity goods with few substitutes (Samuelson & Nordhaus, 2010).
Demand for Inferior Goods
For inferior goods, demand increases as income decreases. This implies the coefficient on income in the demand function, am, is negative. Conversely, if demand decreases as income increases, this confirms its inferior status.
Market Interventions: Price Ceilings and Floors
Price ceilings below equilibrium induce shortages, while floors above equilibrium cause surpluses. These policies aim to regulate prices but often lead to allocative inefficiencies and market distortions (Bishop & Walker, 2019).
Economies and Diseconomies of Scale
Larger firms may experience diseconomies of scale, where per-unit costs increase beyond a certain output level due to managerial or operational complexities. Recognizing these effects guides optimal firm size decisions (Perloff, 2016).
Cost Complementarities
Cost complementarities occur when increasing the output of one product reduces the marginal cost of producing another, indicating synergy in production processes. This concept is vital in multi-product firms seeking to optimize output levels (Tirole, 2017).
Income Elasticity's Business Implications
With an income elasticity of 1.7, a 4% income increase will lead to a 6.8% rise in coffee demand, illustrating how consumer buying behavior changes with income expansions. This insight helps in strategic marketing and sales forecasting (Hirsch, 2018).
Cross-Price Elasticity Application
Given a cross-price elasticity of 4, a 10% change in the price of good Y would result in a 40% change in the demand for good X, demonstrating the sensitivity of substitute or complementary goods (Mankiw, 2014).