Question

Use the following supply and demand curves to answer the following 5 questions.

Demand:p_g=51-2q_d-.5I-1.5p_a

Supply:p_g=1+3q_s+.1p_s

Where p_g is the price of guns, q_d is the quantity of guns demanded, I is income, p_a is the price of ammo, q_s is the quantity of guns supplied and p_s is the price of steel - which is an input used in the production of guns.

1) Find the equilibrium price and quantity of guns as a function of income, the price of ammo, and the price of steel.

2) If the price of ammo increases, what do we expect to happen to the equilibrium price and quantity of guns sold?

3) What does this imply about the relationship between guns and ammo? Are they complement or substitute goods?

4) If the price of steel decreases, what do we expect to happen to the equilibrium price and quantity of guns sold?

5) Suppose that the price of ammo decreases and the price of steel also decreases. In this scenario, what do we expect to happen to the equilibrium price and quantity? Do we even know for certain?

Answer 1

A) The EQUILIBRIUM at , demand=supply,

51-2q-0.5I-1.5pa=1+3q+0.1ps

50-0.5I-1.5pa-0.1ps=5q

Q=10-0.1I-0.3pa-0.02ps

P=1+3*(10-0.1I-0.3pa-0.02ps)+0.1ps=31-0.3I-0.9pa+0.04

B)There is negitive sign associated with price of ammon,so it means Increase in price of ammo Decrease demand.

Decrease in demand will demand curve to left leading to lower equilibrium price and quantity.

C)There is negitive relationship between price of ammo and demand of guns which means Increase in price of ammo Decrease demand of guns and vice versa ,so guns and ammo are compliment goods.

D)There is positive sign associated with price of supply which tells that Increase in price of steel will increase cost of production, leading higher MC and Decrease in supply.

Decrease in supply will shift supply curve left side and equilibrium price will increase and quantity will decrease.