Agricultural and Applied Economics 215
Assignment #4: Market Equilibrium
Due: Nov. 15, 2010
I would like you to generate WORD and/or EXCEL-type files that contain your answers to
the following questions. Please hand in hard copies of this assignment at the end of class
on Nov 15th. Again, as mentioned in the syllabus, no late assignments will be accepted.
To receive full credit you must show all of your work
(115 Total Points)
1. (20 pts) Assume that the market demand and supply curves for No. 2 yellow corn can be
represented via the following:
QD = 250-50PC
QS=25+25PC where PC is the corn price ($/bushel) and Q is the quantity
of corn (millions bushels).
a) (10 pts) What is the equilibrium price, PC* and quantity, Q* of corn
b) (5 pts) Using Excel or some other spreadsheet program verify your answer to a) graphically.
c) (5 pts) Suppose the equilibrium price increased by 50% due to fears of future corn
shortages. Given the above equations, does this new price generate a surplus or shortage
of corn? What is the magnitude of this surplus or shortage?
2. (30 pts) Suppose you have the following market demand (QD) and supply (QS) curves for a
perfectly competitive industry
QD = 200 - 2P + ½Y
QS = -100 + 3P
where Y is the level of per capita household income ($1,000)
a) (15 pts) What is the relationship between income and equilibrium (i) price and (ii)
quantity in this market? That is, how much in general does equilibrium price change for a
given change in income? How much in general does equilibrium quantity change for a
given change in income? (Hint: I want specific equations showing the relationship
between equilibrium price and income and between equilibrium quantity and income).
b) (5 pts) What is equilibrium price and quantity when income = $10,000? What is
equilibrium price and quantity when income is $40,000? (Important: Remember the
income units in the demand function) .
c) (10 pts) Verify graphically both results you obtained in (c) via the use of a single graph.
3. (40 pts) Suppose you have the following supply and demand functions in a perfectly
competitive industry
QD = 50 – P
QS = 20 + 2P
a) (5 pts) What is the equilibrium price and quantity?
b) (15 pts) Suppose the Federal Government, to help offset the Federal deficit, imposes an
excise tax on all products sold. That is, there is a tax of $T per unit of commodity sold.
What is the relationship between equilibrium price and the amount of tax (i.e., specific
equation for a tax of $T/unit)? What is the relationship between equilibrium quantity and
the amount of tax (i.e., specific equation for a tax of $T/unit)? What will be the impact on
equilibrium price and quantity relative to the no tax results given a tax of $T?
c) (10 pts) Assume the tax is $3 per unit of good sold. What is the price paid by consumers
and associated quantity sold? What is the price received by producers (Hint: What is the
relationship between equilibrium price and tax obtained above? Also note that the
difference between what price consumers pay – price suppliers receive = total tax.).
4. (25 pts) Suppose the demand and supply curves for a product are given by:
QD = 500 - 5P
QS = 100 + 5P
a) (5 pts) Determine numerically the market equilibrium price and quantity.
b) (5 pts) If the current market price of the product is $50, what is the quantity supplied and
quantity demanded? How would you describe this situation and what would you expect to
happen in this market?
c) (10 pts) Demand shifts down (↓’s) by 20% due to a ↓ in consumer income and the supply
shifts down (↓ in cost) by 30% due to the adoption of a new technological advance (capital
investment). Evaluate numerically the effects on equilibrium price and quantity of shifts
of supply and demand compared to part (a) above.
d) (5 pts) Given the results in a) and c) should the firm invest on this new technology? (Hint:
How do we evaluate producer welfare?)