Question

The demand for yak butter is given by 150 – 3pd and the supply is 3ps – 30, where Pa is the price paid by demanders and ps is the price received by suppliers, measured in dollars per hundred pounds. Quantities demanded and supplied are measured in hundred-pound units. (1) On a graph, draw the demand curve and the supply curve for yak butter. (2)Write down the equation that you would solve to find the equilibrium price (3) What is the equilibrium price of yak butter? What is the equilibrium quantity? Locate the equilibrium price and quantity on the graph, and label them pı and qı. (4) A terrible drought strikes the central Ohio steppes, traditional homeland of the yaks. The supply schedule shifts to 3ps – 90. 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. (5) What is the new equilibrium price and quantity? Locate the new equilibrium price and quantity on the graph and label them p2 and 02. (6) The government decides to relieve stricken yak butter consumers and producers by paying a subsidy of $10 per hundred pounds of yak butter to producers. If pd is the price paid by demanders for yak butter, what is the total amount received by producers for each unit they produce? When the price paid by consumers is pd, how much yak butter is produced? (7) Write down an equation that can be solved for the equilibrium price paid by consumers, given the subsidy program. What are the equilibrium price paid by consumers and the equilibrium quantity of yak butter now? (8) Suppose the government had paid the subsidy to consumers rather than produc- ers. What would be the equilibrium net price paid by consumers? What would the equilibrium quantity be?

Answer 1

Answer:

1) Attached

2) 150-3p = 3p-30

3) P=30, Q=60

4) 150-3p = 3p-90

5) P=40 and Q=30

6) Ps=Pd+10

7) P=35, Q=45

8) P=45, Q=45

Explanation:

We can write the equation for the quantity demanded as:

$Q_d=150-3p_d$

And the equation for the quantity supplied as:

$Q_s=3p_s-30$

1) Attached

2) The equilibrium price can be calculated by making the quantity supplied equal to quantity demanded:

$Q_s=Q_d\\\\3p-30=150-3p\\\\6p=150+30=180\\\\p=180/6=30$

3) The equilibrium price is P=30.

The equilibrium quantity can be calculated as:

$Q_s=150-3*30=150-90=60$

The equilibrium quantity is Q=60.

4) The supply now becomes:

$Q'_s=3p_s-90$

The equation for the new equilibrium price is:

$Q_d=Q'_s\\\\150-3p=3p-90\\\\6p=150+90=240\\\\p=240/6=40$

$Qd=150-3*40=150-120=30$

5) The new equilibrium is at p=40 and Q=30

6) They will receive

$p_s=p_d+subsidy=p_d+10$

7)  In this case, the quantity supplied becomes:

$Q_s=3p_s-90=3(p+10)-90=3p+30-90=3p-60$

The new price equilibrium becomes P=35:

$Q_s=Q_d\\\\3p-60=150-3p\\\\6p=150+60\\\\p=210/6=35$

The quantity for this equilibrium is Q=45:

$Q_d=150-3*35=150-105=45$

8) Now, the equations for demand and supply are:

$Q_s=3p-90\\\\Q_d=150-3(p-10)=150-3p+30=180-3p$

The equilibrium price and quantity becomes:

$Q_d=Q_s\\\\180-3p=3p-90\\\\6p=180+90\\\\p=270/6=45\\\\\\Q_d=180-3*45=180-135=45$