Question

Suppose that the supply of lemonade is represented by: QS = 40P where Q is measured in pints and P is measured in cents per pint.

Answer the following questions:
1- If the demand for lemonade is QD = 5,000 − 10P, what is the current equilibrium price and quantity?
2-Suppose that a severe frost in Florida raises the price of lemons, and thus the cost of making lemonade. In response to the increase in cost, producers reduce the quantity supplied of lemonade by 400 pints at every price. What is the new equation for the supply of lemonade?
3- Compute the new equilibrium price and quantity of lemonade after the frost.

Answer 1

1. Equilibrium price = 100 cents per pint, equilibrium quantity = 4,000 pints.

2. New supply equation =
`\(40P - 400\)`.

3. New equilibrium price = 108 cents per pint, new equilibrium quantity = 3,920 pints.

Step-by-step explanation:

1. Equilibrium Price and Quantity:

To find the equilibrium price and quantity, set the quantity supplied equal to the quantity demanded:

`\[ QS = QD \]`

`\[ 40P = 5,000 - 10P \]`

Solve for P:

`\[ 50P = 5,000 \]`

`\[ P = 100 \text{ cents per pint} \]`

Now, substitute this price back into either the supply or demand equation to find the quantity:

`\[ QS = 40P \]`

`\[ QS = 40 * 100 \]`

`\[ QS = 4,000 \text{ pints} \]`

So, the equilibrium price is 100 cents per pint, and the equilibrium quantity is 4,000 pints.

2. New Equation for Supply:

In response to the frost, the new supply equation will be the original supply minus the reduction in quantity supplied at every price:

`\[ \text{New QS} = 40P - 400 \]`

3. New Equilibrium Price and Quantity:

Now, set the new supply equal to the demand:

`\[ \text{New QS} = QD \]`

`\[ 40P - 400 = 5,000 - 10P \]`

Solve for P:

`\[ 50P = 5,400 \]`

`\[ P = 108 \text{ cents per pint} \]`

Now, substitute this price back into the new supply equation to find the quantity:

`\[ \text{New QS} = 40 * 108 - 400 \]`

`\[ \text{New QS} = 3,920 \text{ pints} \]`

So, the new equilibrium price is 108 cents per pint, and the new equilibrium quantity is 3,920 pints.