Question

Part 1:

You are given the following equations that represent a
market:
P=400-4Qd
P= 100+Qs
1. What is the market equilibrium quantity?
2. And what is the market equilibrium price?
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Answer 1

To find the market equilibrium quantity and price, we set the quantity demanded equal to the quantity supplied, solve for the quantity, and then determine the price. The market equilibrium quantity is 60 units, and the equilibrium price is $160.

Step-by-step explanation:

To determine the market equilibrium quantity and market equilibrium price from the given equations, we need to set the quantity demanded (Qd) equal to the quantity supplied (Qs). The equations provided are:

Demand: P = 400 - 4Qd

Supply: P = 100 + Qs

Setting them equal to find the equilibrium (since at equilibrium Qd = Qs):

400 - 4Qd = 100 + Qs

Since Qd = Qs, we can replace Qs with Qd:

400 - 4Qd = 100 + Qd

Adding 4Qd to both sides:
400 = 100 + 5Qd
Subtracting 100 from both sides:
300 = 5Qd

Dividing by 5:

60 = Qd = Qs

Now we'll use the equilibrium quantity to find the equilibrium price. Replacing Qd in the demand equation:

P = 400 - 4(60)

P = 400 - 240

P = 160

Therefore, the market equilibrium quantity is 60 units, and the market equilibrium price is $160.