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

Problem 1.

The above diagram is the PPF that shows different combinations of tables and chairs that Bill can produce, given resources. From the diagram, we see that, to produce 10 extra tables, Bill is giving up 20 chairs. So to produce 1 extra table Bill has to give up 20/10 chairs, i.e. opportunity cost of 1 extra table is 2 chairs.

Again,

to produce 20 extra chairs Bill is giving up 10 tables. So to produce 1 extra chair Bill has to give up 10/20 chairs, i.e. opportunity cost of 1 extra chair is 1/2 table.

No. From the diagram, If Bill produces (20,40) combination of both tables and chairs, he is not utilizing the resources fully. Since PPF shows the different combinations of output of two goods using available resources, and there is full allocation of resources, so at (20,40) there is not full allocation of resources.

(20,60) is the combination of two goods that lies on the PPF which shows if Bill produces 20 tables and 40 chairs, there'll be full allocation of resources.

Problem 2.

At equilibrium,

quantity supplied = quantity demaded. Hence, Q_s= Q_D​​​​​​

2p - 2 = 13 - p or, 2p + p = 13 +2 = 15. Therefore, 3p = 15 or, p = 5. Equilibrium price is $ 5.

Substituting p = 5 in any of the above equations, we get, Q_D = 13 - 5 = 8. Equilibrium quantity is 8 million bushels.

Equilibrium can be shown using supply and demand curves

​​​​​​

If we increase the price by $ 1, we'll get respective quantity supplied and quantity demanded. By substituting p = 6 in Q_D and Q_S equations and we get, Q_D = 7 and Q_S = 10

At equilibrium price and quantity,

Price elasticity of demand = percentage change in quantity demanded / percentage change in price = - [{(8 - 7) / (5 - 6)} × 5/8] = 1/1×5/8 = 0.625

Price elasticity of suppy = percentage change in quantity supplied / percentage change in price = - [{(10 - 8)/(6 - 5)} × 5/8] = 2/1 × 5/8 = 1.25.

From the diagram, After imposition of price floor at $ 7, demand for the commodity falls whereas supply rises, as producers are willing to sell more at new price. Therefore, there arises a situation of surplus (excess of supply over demand) in the market.

At new price of $ 7, quantity demanded is 6 whereas quantity supplied is 12.