Question

7. Consider the market for cheese curds in the fictional town of Willows, WI. Suppose the

demand for cheese curds is represented by

Q_d = 30−4P and the supply of cheese curds is represented by Q_s = 2P

(a) What are the equilibrium price and quantity in this market?

(b) Now suppose the residents of Willows become concerned about a rare, cheese-induced

disease, and demand for cheese curds is half of what it was before. (In other words, at

any given price level, consumers demand half of what they would have before.) What is

the new equilibrium price and quantity? Why is the new equilibrium quantity not simply

half the equilibrium quantity from part (a)?

(c) Going back to the original demand and supply curves from part (a), now suppose that

a breakthrough in cheese curd production doubles the supply of cheese curds. (In other

words, at any given price level, the supply is twice as much as it would have been before.)

What is the new equilibrium price and quantity? Why is the new equilibrium quantity

not simply double the equilibrium quantity from part (a)?

Answer 1

Answer

The equation of the demand for cheese curds;

Q_d = 30 − 4P........(1)

The equation of the supply of cheese curds is;

Q_s = 2P.......(2)

(a) Equilibrium price is $5, and equilibrium quantity is 10 units

At the equilibrium level,

Q_d = Q_s

_$\therefore$ 30 − 4P = 2P

Or, -4P - 2P = - 30

Or, - 6P = -30

Or, P = -30 / -6

Or, P = 5

Putting the value of 'P' in equation(1), we get,

Q_d = 30 − 4 * 5

Or, Q_d = 30 − 20

Or, Q_d = 10

Now, putting the value of 'P' in equation(2), we get,

Q_s = 2 * 5

Or, Q_s = 10

$\therefore$Q_d = Q_s = 10

Thus, the equilibrium price in this market is $5, and equilibrium quantity in this market is 10 units.

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(b) If the demand for cheese curds is half of what it was before, the new equation of demand curve will be;

Q_d = (30 − 4P) / 2

Or, Q_d = 15 - 2P..........(1')

The supply of cheese curds remains same as before.Thus the equation of supply curve is same as;

Q_s = 2P.......(2)

As, at the equilibrium level, Q_d = Q_s,

Thus, we get,

15 - 2P = 2P

Or, - 2P - 2P = -15

Or, -4P = -15

Or, P = -15 / -4

Or, P = 3.75

Putting the value of 'P' in equation(1'), we get,

Q_d = 15 - 2 * 3.75

Or,  Q_d = 15 - 7.5

Or, Q_d = 7.5

Now, putting the value of 'P' in equation(2), we get,

Q_s = 2 * 3.75

Or, Q_s = 7.5

$\therefore$Q_d = Q_s = 7.5

The new equilibrium price is $3.75, and the new equilibrium quantity is 7.5 units.

The new equilibrium quantity is not simply half the equilibrium quantity from part (a), because here only demand for cheese curds is half of what it was before, but the supply of cheese curds remains the same as before. As only the demand for cheese curds has decreased by half but the supply of cheese curds remains the same, the new equilibrium quantity is more than the half(7.510/2) of the equilibrium quantity from part (a). For new equilibrium quantity to be half, like the demand, the supply for cheese curds also should be half of what it was before. For new equilibrium quantity to be half, the supply of cheese curds like the demand for cheese curds, also should be half of what it was before.

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(c) If the supply of cheese curds is double now, the new equation of cheese curds will be;

Q_s = 4P..........(2')

The demand for cheese curds remains same as before. Thus the equation of demand for cheese curds remains same as;

Q_d = 30 − 4P........(1)

As the equilibrium condition requires;

Q_s = Q_d

$\therefore$ 4P = 30 − 4P

Or, 4P + 4P = 30

Or, 8P = 30

Or, P = 30 / 8

Or, P = 3.75

Putting the value of 'P' in equation(2'), we get,

Q_s = 4 * 3.75

Or, Q_s = 15

Now, putting the value of 'P' in equation(1), we get,

Q_d = 30 − 4 * 3.75

Or, Q_d = 30 − 15

Or, Q_d = 15

$\therefore$Q_s = Q_d = 15

Thus, the new equilibrium price is $3.75, and the new equilibrium quantity is 15 units.

The new equilibrium quantity is not simply double the equilibrium quantity from part (a), because here only the supply of cheese curds is twice of what it was before, but the demand for cheese curds remains the same as before. As only the supply of cheese curds has increased by twice but the demand for cheese curds remains the same, the new equilibrium quantity is less than the double(15​​​​​​​10*2) of the equilibrium quantity from part (a). For new equilibrium quantity to be double, the demand for cheese curds like the supply of cheese curds, also should be twice of what it was before.

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