Question

Problem 1

Bill can produce either tables or chairs. Bill can work up to 10 hours a day. His production possibilities are given in the table below:

Tables	Chairs
0	100
10	80
20	60
30	40
40	20
50	0

1. Construct the production possibilities frontier (PPF) for Bill. Put tables on the Horizontal axis and chairs on the vertical axis.

2. What is Bill’s opportunity cost of producing one additional table?

3. What is Bill’s opportunity cost of producing one additional chair?

4. Currently Bill is producing 20 tables and 40 chairs.

1. Is this allocation of resources efficient? Why?

2. Show this allocation on the graph and advise Bill how he can be more efficient.

Problem 2

Suppose the market for corn is given by the following equations for supply and demand:

            QS = 2p − 2

            QD = 13 − p

where Q is the quantity in millions of bushels per year and p is the price.

1. Calculate the equilibrium price and quantity.

2. Sketch the supply and demand curves on a graph indicating the equilibrium quantity and price.

3. Calculate the price-elasticity of demand and supply at the equilibrium price/quantity.

4. The government judges the market price is under expectations and announces a price floor equal to $7 per bushel.

1. Would there be a surplus or a shortage?

2. What would be the quantity of excess supply or demand that results?

3. Use the graph to show you results.

Answer 1

Answer – Suppose the market for corn is given by the following equations for supply and demand:

            QS = 2p − 2

            QD = 13 − p

where Q is the quantity in millions of bushels per year and p is the price.

Equilibrium is attained when demand and supply equal each other i.e., when QS = QD.

Thus, equating QS = QD, we get,

2p – 2 = 13 – p;

Or, 3p = 15;

Or, p* = 5.

Q* = 2Xp* - 2 = 2 *5 – 2 = 8.

Therefore, the equilibrium price = $5 and equilibrium quantity = 8 units.

Below I have graphed the demand and supply curves and indicated the equilibrium in the following graph.

At the equilibrium price and quantity,

the price elasticity of demand (Ed) = dQD/dp X (p*/Q*) = (-1) X (5/8) = -5/8 = 0.625.

At the equilibrium price and quantity,

the price elasticity of supply (Es) = dQS/dp X (p*/Q*) = 2 X 5/8 = 5/4 = 1.25

The government judges the market price is under expectations and announces a price floor equal to $7 per bushel.

A price floor is the minimum price at which a product can be sold. In this case, the government imposes a price floor of $7 per bushel. Since the government has instituted a legal minimum of $7 which is higher than the equilibrium price of $5, the price floor is binding i.e., the forces of demand and supply cannot bring the market price down to equilibrium after $7. Quantity supplied at this price was 12 units and quantity demanded at this price was 6 units.

(a) Since quantity supplied > quantity demanded at this price, this would lead to a surplus.

(b) At this price, quantity demanded = 6 units & quantity supplied = 12 units. Thus, surplus = (12 – 6) units = 6 units.

(c) I have illustrated this in the following graph.