Given the supply equation: Ps = 50 + 5Qs and demand equation: Pd = 120 – 3Qd

Question

• 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

Answer 1

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.