To find the equilibrium price and quantity, we set the supply and demand equations equal to each other:
50 + 5Qs = 120 - 3Qd
Simplifying this equation, we get:
8Qs = 70 - 3Qd
Now, let's solve for Qd to find the quantity at equilibrium:
8Qs + 3Qd = 70
3Qd = 70 - 8Qs
Qd = (70 - 8Qs) / 3
Next, we substitute this value of Qd in either the supply or demand equation to find the equilibrium price. Let's use the demand equation:
Pd = 120 - 3Qd
Pd = 120 - 3((70 - 8Qs) / 3)
Pd = 120 - (70 - 8Qs)
Pd = 120 - 70 + 8Qs
Pd = 50 + 8Qs
Now we have the price at equilibrium: P = 50 + 8Qs.
i) The price at equilibrium is P = 50 + 8Qs.
ii) To calculate consumer surplus (CS), we need to find the area under the demand curve and above the equilibrium price. The formula for CS is:
CS = 0.5 * (P - equil price) * Q
In this case, the equilibrium price is 50 + 8Qs. So, the consumer surplus is given by:
CS = 0.5 * (120 - (50+8Qs)) * Q
iii) To calculate producer surplus (PS), we need to find the area above the supply curve and below the equilibrium price. The formula for PS is:
PS = 0.5 * (equil price - P) * Q
In this case, the equilibrium price is 50 + 8Qs. So, the producer surplus is given by:
PS = 0.5 * ((50 + 8Qs) - (50)) * Q
iv) Social surplus is the sum of consumer surplus and producer surplus:
Social Surplus = CS + PS
v) To illustrate the consumer surplus and producer surplus on a graph, we can plot the demand and supply curves, and shade the areas representing the CS and PS.
Given the supply equation: Ps = 50 + 5Qs and demand equation: Pd = 120 – 3Qd
• Calculate
• i) The price at equilibrium
• ii) Consumer surplus /CS
• iii) Producer surplus/PS
• iv) Social surplus
• v) Using a graph illustrate the CS&PS
1 answer