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Suppose the demand function​ (D) for golf clubs​ is: Q​P, where P is the price paid by consumers in dollars per club and Q is the quantity demanded in thousands. Suppose the supply curve​ (S) for golf clubs is estimated to​ be: QP. Calculate the equilibrium price for golf clubs and the equilibrium quantity sold. The equilibrium price is ​$ 75 per club ​(Enter your response as an​ integer.)​, and the equilibrium quantity is 75 thousand clubs ​(Enter your response as an integer.​) Suppose instead that golf club producers agree to charge a price of ​$ per club. This would result in a surplus of nothing thousand clubs ​(Enter your response as an integer.​)

Respuesta :

MrRoyal

Answer:

(a)

The equilibrium price is $75 per club

The equilibrium quantity is 75000 clubs

(b)

A charge a price of $​50 per club. This would result in a surplus of 25000 clubs

Explanation:

Given

[tex]Q = 150 - 1.00P[/tex] --- The demand function

[tex]Q = 1.00P[/tex] --- The supply function

Solving (a): The equilibrium price and quantity

To do this, we equate both functions

This gives:

[tex]1.00P = 150 - 1.00P[/tex]

Collect like terms

[tex]1.00P+1.00P = 150[/tex]

[tex]2.00P = 150[/tex]

Make P the subject

[tex]P =\frac{150}{2.00}[/tex]

[tex]P = \$75[/tex] ---The equilibrium price

Substitute 75 for P in [tex]Q = 1.00P[/tex]

[tex]Q = 1.00 * 75[/tex]

[tex]Q = 75[/tex] ---- The equilibrium quantity

Solving (c): When the price is changed to $50

This means that: [tex]P =50[/tex]

The quantity demanded will be:

[tex]Q = 150 - 1.00P[/tex]

[tex]Q = 150 - 1.00 * 50[/tex]

[tex]Q = 150 - 50[/tex]

[tex]Q = 100[/tex]

Subtract the equilibrium quantity from [tex]Q = 100[/tex]  to get the shortage/surplus

[tex]\triangle Q = 100 - 75[/tex]

[tex]\triangle Q = 25[/tex]

Since the change is positive, then there is a surplus.

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