The demand and supply equations for the pear market are: Demand: P = 12 - 0.01Q

ID: 1225386 • Letter: T

Question

The demand and supply equations for the pear market are: Demand: P = 12 - 0.01Q Supply: P = 0.02Q where P= price per bushel, and Q=quantity.

a. Calculate the equilibrium price and quantity.

b. Suppose the government guaranteed producers a price of $20 per bushel. What would be the effect on quantity supplied? Provide a numerical value.

c. By how much would the $20 price change the quantity of apples demanded? Provide a numerical value.

d. Would there be a shortage or surplus of apples?

e. What is the size of this shortage or surplus? Provide a numerical value.

a) At Equilibrium,

Demand = Supply

12 - 0.01 Q = 0.02 Q

0.03 Q = 12

Q = 400 Units

Conclusion:- Equilibrium Quantity = 400 Units and Equilibrium Price = 0.02 * 400 = $ 8 .

b) The Quantity Supplied when the government guaranteed producers a price of $20 per bushel:-

Quantity Supplied = 20 / 0.02 = 1000 Units

Conclusion:- Quantity Supplied of apples = 1000 Units

c) The Quantity Demanded when the government guaranteed producers a price of $20 per bushel:-

Quantity Demanded is given by following equation in question:-

P = 12 - 0.01 Q [Putting the value of P = $ 20, We will get Quantity demanded.]

20 = 12 - 0.01 Q

0.01 Q = 12 - 20

Q = (-) 8 / 0.01 = (-) 800

As the Quantity can not be in negative, thus ignoring the minus sign here, Quantity Demanded = 800 Units.

Conclusion:- Quantity of apples demanded = 800 Units

d) The Quantity Supplied of apples > The Quantity demanded of apples, Thus there would be a Surplus of apples.

e) Size of Surplus = 1000 - 800 = 200 Units

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