Juan mows lawns in his neighborhood for extra money. Suppose the demand for lawn mowing in Joe’s neighborhood is: QD = 48 – 2P and that the supply of lawn mowing (Juan’s willingness to mow lawns) is: Qs = -12 + P. The market-clearing price of lawn mowing is $____ per lawn and the market-clearing quantity is ____ lawns. The corresponding consumer surplus is $____.
Market Clearing Price: $20
Market Clearing Quantity: 8 Lawns
Consumer surplus: $16.00
To find the market-clearing price and quantity, we need to set the quantity demanded equal to the quantity supplied.
Given:
Demand: QD = 48 - 2P
Supply: Qs = -12 + P
Setting QD equal to Qs:
48 - 2P = -12 + P
Adding 2P on both sides:
48 = -12 + 3P
Adding 12 on both sides:
60 = 3P
Dividing by 3:
P = 20
Now, we can substitute the price value of $20 into either the demand or supply equation to find the quantity.
Using the demand equation:
QD = 48 - 2(20)
QD = 48 - 40
QD = 8
So, the market-clearing price is $20 per lawn and the market-clearing quantity is 8 lawns.
To find the consumer surplus, we need to find the area below the demand curve and above the market-clearing price.
The formula for consumer surplus is: Consumer Surplus = 1/2 * (QD * PD - QD * P)
Using the values we found:
Consumer Surplus = 1/2 * (8 * 20 - 8 * 20) = 1/2 * (160 - 160) = 1/2 * 0 = 0
Therefore, the corresponding consumer surplus is $0.
To find the market-clearing price and quantity, we need to find the equilibrium point where the quantity demanded (QD) is equal to the quantity supplied (QS).
Step 1: Set QD equal to QS and solve for the price (P).
QD = QS
48 - 2P = -12 + P
Step 2: Solve for P to find the market-clearing price.
48 + 12 = 2P + P
60 = 3P
P = 20
Step 3: Substitute the market-clearing price (P = $20) into either the demand or supply equation to find the market-clearing quantity.
QD = 48 - 2P
QD = 48 - 2(20)
QD = 48 - 40
QD = 8
So the market-clearing price is $20 per lawn and the market-clearing quantity is 8 lawns.
Now, let's calculate the consumer surplus.
Consumer surplus is the difference between what consumers are willing to pay for a product and what they actually pay. It represents the benefit consumers receive from purchasing a good at a price lower than their maximum willingness to pay.
Step 4: Calculate consumer surplus using the formula:
Consumer Surplus = (1/2) * (Quantity Purchased) * (Difference between maximum willingness to pay and actual price)
Here, the maximum willingness to pay (P) is $48 - QD, as given by the demand equation.
Consumer Surplus = (1/2) * (QD) * (Maximum willingness to pay - Actual Price)
Consumer Surplus = (1/2) * (8) * (48 - 20)
Consumer Surplus = (1/2) * 8 * 28
Consumer Surplus = 112
Therefore, the corresponding consumer surplus is $112.