Consider two equations describing the relationship between three variables X$,$ Y$1,$ and Y$2$:

X $=$ a $+$ b Y$1,(1)$

X $=$ c $$ d Y$2,(2)$

where a$,$ b$,$ c$,$ and d$,$ are positive, known constants $($numbers$).$ The objective is to find values of X$,$ Y$1,$

and Y$2$ for which both equations are satisfied and as well Y$1=$ Y$2.$

expressions $(1)$ and $(2)$ to solve

for X$.$

c$.$ After solving for X$,$ find the values of Y$1$ and Y$2$ and verify whether the third equation is satisfied.

d$.$ Now, rename Y$1$ as QS representing quantity supplied, replace a with $200,$ replace b with $2,$

rename Y$2$ as QD representing quantity supplied, replace c with $400,$ replace d with $3,$ and rename

X as P representing price. This gives you a system of supply and demand for a good. Re$-$write

expressions $(1)$ and $(2)$ using this information. How many unknown variables and how many

equations do you have?

e$.$ To find the equilibrium and solve for equilibrium values of QD$,$ QS$,$ and P$,$ what other condition

do we need? $[$Hint: Think about our discussion in class and the fill the blank here to find out

what other condition you might need: $$If quantity demanded is more than quantity supplied, the

price will $\_\_\_\_\_\_\_\_.$ If quantity demanded is less than quantity supplied, then price will

$\_\_\_\_\_\_\_\_\_.$ So$,$ price will not change only if quantity demanded $\_\_\_\_\_\_\_\_\_$ quantity supplied.

This is how we define equilibrium: a condition under which variables in the model remain stable

and do not change. We call this additional equation market$-$clearing condition.$]$

f$.$ Given the system of supply and demand and the market$-$clearing condition, solve for equilibrium

values of QD$,$ QS$,$ and P$.$

g$.$ Show the supply and demand curves on a grid, putting price on the vertical axis and clearly

identify the equilibrium price and quantity.

h$.$ What is the quantity supplied and demanded at P $=290?$ Excess supply or excess demand, which

one exists at this price and what is the size of it$?$ How is expected to affect the price? How is the

induced change in price expected to affect quantities demanded and supplied?

i$.$ What is the quantity supplied and demanded at P $=220?$ Excess supply or excess demand, which

one exists at this price and what is the size of it$?$ What are the expected impacts on the variables

of the model?

j$.$ Based on the concepts of excess supply and excess demand and how they put upward or

downward pressures on price argue why any price other than the one you identified in $($f$)$ cannot

establish equilibrium