Question

ECON 2012 Homework 4 Due: 3/5 P=3Q+15 and P=-Q+ 55 1. Identify which equation is supply and which one is demand. How do you know? 2. Calculate the equilibrium price and quantity. 3. Draw a graph depicting consumer and producer surplus at the equilibrium 4. Interpret what is meant by producer surplus and explain how it is calculated. 5. Calculate the social surplus at equilibrium 6. Draw another graph indicating a decrease in supply and provide 2 examples of what could cause this change. 7. What happens to quantity demanded due to this change? What economics terminology would you use to describe it?

Answer 1

Q1) Price and quantity demand have an inverse relationship, that is, as price increases quantity demanded decreases, cetris paribus

While, Price and quantity supplies have a direct relationship, that is, as price increases quantity supplied increases, cetris paribus

So P=3Q+15 shows a direct relation and ins therefore the supply equation while P=-Q+55 shows an inverse relationship, and is therefore the demand equation

Q2) Equilibrium can be achieved at by equating the two equations:

3Q+15 = -Q+55

=> 4Q = 40

=> Q = 10

So the equilibrium is at a quantity of 10 units and the price will be P = 3 x 10 +15 = $45

Q3)

We need to take a few data points satisfying the two equations:

Price	QD	QS
36	19	7
39	16	8
42	13	9
45	10	10
48	7	11
51	4	12

We then plot the graphs:

Price 6 8 10 14 16 18 12 Quantity D +-os

CS = Consumer surplus, PS = Producer surplus

4) Producer surplus stands for the difference between the price at which the supplier is willing to sell and the price at which he actually sells.

At equilibrium price, he gets $45 per unit while, he would sell 0 units at a price of 15, derived from P = 3(0) +15 so the  producer surplus would be 1/2 x Q x (Eqiulibrium price - Price of 0 units)

Producer surplus = 1/2 x 10 x (45-15)

Producer surplus = 1/2 x 10 x (30) = 150

Answer 2

(1) P = 3Q + 15 is the supply equation as the slope is positive (which denotes a positive/direct relationship between price and quantity) and P = -Q+55 is the demand equation since the slope is negative (which denotes a negative/inverse relationship between price and quantity) .

(2) At equilibrium, supply = demand => 3Q + 15 = -Q + 55 => 3Q+Q = 55-15 => 4Q = 40 => Q = 10

Now P = 3Q + 15 = 3(10)+15 = 45

Price can be derived from the demand equation too, i.e., P = -10+55 = 45

Hence, the equilibrium quantity = 10 and equilibrium price = 45

(3) As shown below, the equilibrium quantity = 10 and equilibrium price = 45. And the area of the triangle ABE (grey shaded area) refers to the consumer surplus, which measures the difference between consumers' willingness to pay and they actually pay. On the other hand, the orange share area (triangle BCE) represents the producer surplus which measures the amount the producer actually gets and the cost the producer incurs.

Price 0 5 10 15 20 Quantity 25 30 35 40

(4) As described in (3), the producer surplus is measured by the area of the triangle BCE. In the present case, producer surplus = 0.5 * BC * BE, where BC is the distance between equilibrium price and intercept of the supply curve, i.e., 45 - 15 = 30 and BE = distance from the origin to the equilibrium output, i.e., BE = 10. Hence, producer surplus = 0.5*30*10 = 150

(5) Social surplus in this case would be the surplus for consumers and surplus for producer. We can calculate consumer surplus by area of triangle ABE = 0.5*AB*BE, where AB = intercept of demand curve - equilibrium price = 55-45 = 10 and BE = 10 as explained in (4). Hence, consumer surplus = 0.5*10*10 = 50.

Hence, total social surplus = producer surplus (calculated in 4) + consumer surplus = 150 + 50 = 200

(6) A decrease in supply can be depicted by a leftward shift of the supply curve, from S to S' as shown in the diagram below.

Price 5 10 15 25 30 35 40 20 Quantity

Several factors can cause such a shift in supply such as low production, political unrest, war etc.

(7) When supply decreases as shown above, a new equilibrium is attained with a higher price and hence quantity demanded decreases as shown in the above diagram.