HW # 1: PROBLEM SET

Demand and Supply

Let the Market Demand curve for soybeans be given by the following equation:

Q = 100,000 10,000P

WhereQ = the quantity of soybeans in kilograms

P = the price of soybeans in dollars per kilogram.

Let the Market Supply curve for soybeans be given by the equation:

Q = 5,000 + 5,000P

1. Roughly graph the Demand Curve on a sheet of paper.Be sure to label the axes.What is the slope of the Demand Curve?Is it positive or negative?Why?What is the intercept?Note that in order to calculate the intercept and slope you probably want to rewrite the equation so that P is expressed in terms of Q.

2. Graph the Demand and Supply curves together.Label all parts of the graph.Using algebra, solve for the equilibrium price and quantity of soybeans.

3. Compute the consumer surplus (CS) and producer surplus (PS).The Consumer Surplus (CS) is the triangular area under the demand curve and above the equilibrium price.Solve for the consumer surplus at the equilibrium price and quantity.(Hint: Use the formula for the area of a triangle.)The Producer Surplus (PS) is the triangular area above the supply curve and below the equilibrium price.Solve for the producer surplus at equilibrium price and quantity.(Again, use the formula for the area of a triangle.)

4. Assume that the government creates price controls for soybeans in order to help the poor by holding prices low.Assume that these price controls take the form of a price ceiling in which the government prohibits the price of soybeans from rising above $5.00 per kilogram.Draw a diagram.What will be the quantity of soybeans supplied?What will be the quantity of soybeans demanded?What will be the result of this price ceiling? In what quantity?

5. Assume that the government creates price controls for soybeans in order to help the farmers by holding prices high.Assume that these price controls take the form of a price floor in which the government prohibits the price of soybeans from falling below $8.00 per kilogram.Draw a diagram.What will be the quantity of soybeans supplied?What will be the quantity of soybeans demanded?What will be the result of this price floor?In what quantity?