Managerial Economics Homework

  
1. Do your research on the market for palladium. Is it appropriate to use the Supply and Demand model to predict price movements in the market for palladium? What would be your criterion for deciding whether it is appropriate? (There is no unique best answer to this question; your score depends on your reasoning. You may wish to use information presented in the lecture.)
2. In a competitive market, suppose that the demand function is QD(P) = 34−(P/2) and the supply function is QS(P) = 5P −10.
(a) What is excess supply or excess demand at a market price of P=6?
(b) If the market price is P=6, then how much is actually bought and sold in the market? From this starting point, what in this market do you expect to change over time? In your answer, what are you assuming about what is endogenous and what is exogenous?
(c) Draw the supply and demand curves, showing the exact coordinates of at least two points on each curve.
(d) Calculate the equilibrium price and quantity.
(e) Calculate the inverse supply and demand curves.
(f) Use calculus to determine the slopes of the supply and demand curves.
3. In the competitive market for welding services in Logan, assume that a > 0 and b > 0 are exogenous variables: a represents the price of a related good, and b represents the number of welders (i.e., sellers) in the market. Q represents hours of welding services, and P represents a welder?s hourly wage. Assume that the demand for welding services is
QD(P) = a−
P 2
and the supply is
QS(P) =
b(P −2) 20
(a) Which of the following possibilities makes sense, for the related good? Briefly justify your answers.
i The related good is a substitute for welding.
ii The related good is a complement for welding.
iii Welding is an input in the manufacture of the related good.
iv The related good is something used in the process of welding.
The baseline case in this market is: a=34 and b=100.
(b) Draw the supply and demand curves in the baseline case, including the exact coordinates of two points on each curve.
(c) Starting from the baseline case, suppose that the price of the related good falls to a = 23, and the market reaches equilibrium. On the same diagram draw (i) the new supply and demand curves, including the exact coordinates of two points on each curve. (ii) Calculate price and quantity in the new equilibrium.
(d) Starting from the baseline case, suppose that the number of welders in the market rises to b = 122, and the market reaches equilibrium. On a new diagram draw (i) the new supply and demand curves, including the exact coordinates of two points on each curve. (ii) Calculate price and quantity in the new equilibrium.
(e) Describe an economically reasonable model in which a would rise. Describe, alternatively, an economically reasonable model in which a would fall.
(f) Starting from the baseline case, assume that a falls to a=19, but assume also that the number of welders b adjusts until the equilibrium wage is unchanged. (i) In this problem, what is exogenous and what is endogenous? (ii) What is the new number of welders? (iii) What has happened to the equilibrium quantity of welding services, per welder? Is it higher or lower than in the baseline case? (iv) Can you provide an intuitive explanation for your answer to (iii)? (Think about the individual welder?s supply decision.)
(g) Starting from the baseline case, suppose that a changes as in part (c) and b changes in part (d), simultaneously. Calculate price and quantity in the new equilibrium. Is there any reasonable sense in which one can say that the supply shift dominates the demand shift, or the demand shift dominates the supply shift? (Look at the change in the equilibrium quantity as result of the shifts in supply and demand)

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