For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price.
p = - 2x + 15 and p = 5x + 1
a. equilibrium quantity 4,000 units; equilibrium price $11
b. equilibrium quantity 4,000 units; equilibrium price $9
c. equilibrium quantity 2,000 units; equilibrium price $9
d. equilibrium quantity 2,000 units; equilibrium price $11
thank you for helping
equilibrium quantity is where supply = demand:
-2x+15 = 5x+1
x = 2
so, p=11
Looks like D to me
5. (30 points)
The demand for lithium is given by P = 500 – 0.2L, where L is the quantity of mined lithium and
P is the price. Lithium is mined at a constant marginal cost of $50 and sold in a competitive
market.
a) What is the quantity of lithium sold in equilibrium?
b) If lithium mining generates a marginal external cost of $0.1L, what is the socially optimal
level of lithium?
c) Draw a diagram illustrating the private and social marginal cost curves, and the demand curve.
Determine and place on the diagram the private market quantity, the socially optimal quantity,
and the social welfare cost.
To find the equilibrium quantity and price, we need to set the supply and demand equations equal to each other and solve for x, which represents the quantity demanded in units of 1,000.
Setting the two equations equal to each other:
-2x + 15 = 5x + 1
Simplifying the equation:
15 - 1 = 5x + 2x
14 = 7x
Solving for x:
x = 14/7
x = 2
Now that we have found x, we can substitute it back into either of the original equations to find the equilibrium price.
Using the first equation p = -2x + 15:
p = -2(2) + 15
p = -4 + 15
p = 11
Therefore, the equilibrium quantity is 2,000 units (2*1,000) and the equilibrium price is $11. Hence, the correct answer is option a. equilibrium quantity 4,000 units; equilibrium price $11.
To find the equilibrium quantity and price, we need to set the supply and demand equations equal to each other and solve for x.
Equating the two equations, we have:
-2x + 15 = 5x + 1
Now, we can solve for x:
-2x - 5x = 1 - 15
-7x = -14
Dividing both sides by -7:
x = -14/-7
x = 2
So, the equilibrium quantity is 2,000 units.
To find the equilibrium price, we substitute the value of x back into either the supply or demand equation. Here, we can use the demand equation p = -2x + 15:
p = -2(2) + 15
p = -4 + 15
p = 11
Therefore, the equilibrium price is $11.
So, the correct answer is option (a) equilibrium quantity 4,000 units; equilibrium price $11.