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NAME: ________________________ PSU Email: [email protected] Homework #1 Intermediate Microeconomics ECON 302, Section 001 Due: Wednesday, September 7th, 2016 at 8:00AM 1. (1 Point) Please initial that you understand each of the following statements. Failure to complete this will result in a one point deduction. ____ The assignment is open book/open note. Students may discuss this assignment with other students in the class, but must turn in legible, handwritten, and original answers. The posting of questions from this assignment to an online forum like Chegg or Coursehero will be considered cheating. Answers closely matching replies to such a post will be scrutinized. Students caught cheating will receive a zero on the assignment and may receive additional punishment under Faculty Senate Rule 49†20. ____ This assignment must be turned in at the beginning of class on Wednesday, September 7th. It will be considered late once the instructor starts lecturing. Late assignments will not be accepted and students will receive a score of zero on that assignment. ____ All work must be stapled, in the proper order, in the upperâ€left corner of the paper prior to being submitted. One point will be deducted if the instructor staples or restaples the work for you. ____ Your name and Penn State Email must appear at the top of the first page. ____ Be sure to fully answer the entire question. Some questions have multiple parts which ask you to explain your reasoning. Providing the correct answer without an explanation (when asked for) will not earn students full credit. ___ Numbers should be rounded to two decimal places if needed.
2. Assume the market demand for a product is PQD 2.0000,1 and the market supply is 1,0002PQS .
A. (1 Point) State the inverse supply function: __________________________.
B. (1 Point) State the inverse demand function: ___________________________.
C. (4 Points) Solve for the market equilibrium price and quantity. Price = __________ Quantity = __________
D. (1 Point) Assume that this product is a normal good. An increase in income causes demand for the product to increase by 100 units at every potential price. What is the new demand function?
Demand: _______________________________
E. (1 Point) Given the change in Part D, what is the new inverse demand function? Inverse Demand Function: ___________________________
F. (4 Points) Solve for the new equilibrium price and quantity that occurs after the change in income. Price = __________ Quantity = __________
G. (4 Points) Graph the market before and after the change in income. Label all curves and equilibria fully.
3. (2 Points) Assume the supply of widgets is explained by the following function, PS PPQ 25.010 where PP represents the price of plastic, the key input required to produce widgets. Explain in words how a $2 increase in the price of plastic will affect the supply of widgets.
4. Assume that the supply and demand for a product are defined by the following functions: Supply: COMPS PPQ 3105.0 , where COMPP represents the price of a complement in production Demand: PQD 440 A. (4 Point) Solve for the equilibrium price and quantity in this market. Hint: Your answers will be functions of COMPP. Price = __________________________ Quantity = _______________________
B. (2 Points) Explain in words how an increase in COMPP will affect the equilibrium price and quantity of this product.
C. (4 Points) Graph the market equilibria for this product when COMPP increases from $5 to $10. Be sure to fully label your graph and all relevant supply and demand curves.
5. In class we derived a general solution for the equilibrium price such that: s ds d ds A BB A BB P ¸Ì§ ¹ · ¨Ìˆ © § ¸Ì§ ¹ · ¨Ìˆ © § 11* After some additional algebra, it can be shown that the equilibrium quantity takes on a value of: s ds d d ds s A BB B A BB B Q ¸Ì§ ¹ · ¨Ìˆ © § ¸Ì§ ¹ · ¨Ìˆ © § .
A. (1 Point) Define the following parameters based on how they were introduced in class: :SB :DB B.
Assume that both supply and demand increase. What condition must hold in order for us to be certain that the equilibrium price will increase as a result of this simultaneous shift? Be sure to state your answer in terms of the appropriate parameters in P and Q.
Paper For Above instruction
The assignment covers fundamental concepts in microeconomic analysis, including market equilibrium, shifts in supply and demand, the effect of input prices, and the comparative statics of simultaneous shifts. This essay will systematically address each question to elucidate the mechanics of market interactions and the implications of various economic changes.
Initially, students are asked to demonstrate comprehension of administrative instructions, but the core economics problems involve deriving and analyzing supply and demand functions, calculating equilibrium conditions, and understanding shifts in market equilibria. This foundational knowledge forms the basis for understanding how markets operate and respond to external changes, such as income increases or input price variations.
The first substantive question involves deriving the inverse supply and demand functions from given equations, and solving for the equilibrium price and quantity in the market. In microeconomics, the inverse functions are especially useful because they express price as a function of quantity, enabling easier analysis of equilibria. To find the equilibrium, set the demand equal to supply and solve the resulting equations algebraically. These steps clarify how equilibrium prices and quantities are determined directly from the demand and supply equations.
Next, the problem considers the effect of an income increase on demand for a normal good. Since demand shifts outward uniformly, the new demand function reflects this increase, which in turn influences the new equilibrium. Calculating the new inverse demand function involves incorporating the change directly into the original demand equation, illustrating how consumer income affects market outcomes.
Graphing the market before and after the income change visually demonstrates the shifts in the demand curve and the subsequent change in equilibrium. Fully labeling these curves highlights the dynamic nature of markets and the impacts of external factors.
Further, the assignment probes the influence of input prices on supply, specifically analyzing how a rise in the price of plastics affects the supply of widgets. An increase in input costs usually causes the supply curve to shift inward, reducing supply at any given price, thereby raising equilibrium prices and lowering quantities if all other factors are held constant.
The analysis extends to a model with complementary goods in production, where the supply function depends on the price of a complement (COMPP). Solving for equilibrium allows understanding how changes in the price of the complementary good affect the primary market's balance. An increase in the price of the complement generally influences both the equilibrium price and quantity, either positively or negatively, depending on whether the complement is a substitute or a complement in production.
The general algebraic derivation of equilibrium price and quantity involves understanding the parameters that govern shifts in supply and demand, emphasizing the conditions under which simultaneous changes lead to predictable price movements. Specifically, these conditions depend on the relative magnitude of shifts in supply and demand, which are captured by the parameters introduced during the derivation.
Overall, this assignment emphasizes the critical importance of mathematical modeling and graphical analysis in understanding microeconomic dynamics. Recognizing how shifts in input costs, consumer income, and related markets influence equilibrium conditions equips students with the analytical tools necessary for advanced economic analysis and policy evaluation.