Solve these demand and supply questions: a. The demand function for commodity is…

Solve these demand and supply questions:
a. The demand function for commodity
is
, where
is the price paid by consumers. The supply function for
is
, where
is the price received by suppliers. For each unit sold, the government collects a tax equal to half of the price paid by consumers. Find the equilibrium prices and quantities. (Hint: in equilibrium, supply must equal demand).
b. The demand for yak butter is given by
and the supply is
, where
is the price paid by demanders and
is the price received by suppliers, measured in dollars per hundred pounds. Quantities demanded and supplied are measured in hundred-pound units. Draw the demand curve (with blue ink) and the supply curve (with red ink) for yak butter.
c. Write down the equation that you would solve to find the equilibrium price. What is the equilibrium price of yak butter? What is the equilibrium quantity? Label the equilibrium price and quantity on the graph
and
.
Using the same set up and graphs as in question 9 , answer these questions:
a. A terrible drought strikes the central Ohio steppes, traditional homeland of the yaks. The supply schedule shifts to
. The demand schedule remains as before. Draw the new supply schedule. Write down the equation that you would solve to find the new equilibrium price of yak butter. What is the new equilibrium price and quantity. Locate the new equilibrium price and quantity on the graph and label them
and
.
b. The government decides to relieve stricken yak butter consumers and producers by paying a subsidy of
per hundred pounds of yak butter to producers. If
is the price paid by demanders for yak butter, what is the total amount received by producers for each unit they produce? Whe paid by consumers is
, how much yak butter is produced?