Question

The demand for cereal is described by the equation Q-20-0.5p+10 Ps, and the supply is Q-4-2p-3P where PB is the price of bread and PS is the price of sugar. a. If the price of bread PB-1 and the price of sugar PS-2, find the equilibrium price and quantity. Show your answer using a graph. Graph the demand and supply curve as well as the equilibrium price and quantity. Scale: x axis: 1 square-2units; y scale: 1 square-5 units. b. Estimate the price elasticity of demand at the equilibrium price and quantity. c. Estimate the price elasticity of supply at the equilibrium price and quantity. d. Estimate the cross elasticity of demand between the price of bread and the quantity of cereal. e. Using the sign of the cross elasticity, can you infer if bread and cereal are complements or substitutes?

Answer 1

To solve this problem, we'll substitute the given values of PB and PS into the demand and supply equations and solve for equilibrium price and quantity. Then, we'll plot the demand and supply curves on a graph to find the intersection point, which represents the equilibrium.

a. Given:
PB = 1 (Price of bread)
PS = 2 (Price of sugar)

Demand equation: Q = 20 - 0.5P + 10PS
Substituting PB = 1 and PS = 2:
Qd = 20 - 0.5P + 10(2)
Qd = 20 - 0.5P + 20
Qd = 40 - 0.5P

Supply equation: Q = 4 - 2P - 3PS
Substituting PB = 1 and PS = 2:
Qs = 4 - 2(1) - 3(2)
Qs = 4 - 2 - 6
Qs = -4

Now we can find the equilibrium price by equating the quantity demanded (Qd) and quantity supplied (Qs):
40 - 0.5P = -4
0.5P = 44
P = 88

So the equilibrium price is P = 88.

Now we can substitute this equilibrium price into the demand equation to find the equilibrium quantity:
Qd = 40 - 0.5(88)
Qd = 40 - 44
Qd = -4

The equilibrium quantity is Q = -4.

Now, let's plot the demand and supply curves on a graph:

```plaintext
Price (P)
^
|
| D
|
| S
|
|_____________________
Quantity (Q)
```

The demand curve (D) will be a downward-sloping line passing through the point (88, -4) on the graph.

The supply curve (S) will be an upward-sloping line passing through the point (88, -4) on the graph.

The equilibrium point is where the demand and supply curves intersect, which in this case is at the coordinates (88, -4).

b. To estimate the price elasticity of demand at the equilibrium price and quantity, we need to calculate the percentage change in quantity demanded divided by the percentage change in price. However, since the given quantity is negative (-4), we cannot calculate the elasticity accurately. The negative sign indicates that the equilibrium quantity is below the y-axis, suggesting that there is no real equilibrium in this case.

c. Similarly, we cannot estimate the price elasticity of supply accurately since the equilibrium quantity is below the y-axis.

d. The cross elasticity of demand between the price of bread (PB) and the quantity of cereal (Q) can be estimated using the formula: (ΔQd/ΔPB) * (PB/Qd).

Since we cannot calculate the exact values for the changes in price and quantity, we cannot estimate the cross elasticity accurately.

e. Based on the given information, we cannot infer whether bread and cereal are complements or substitutes since we do not have the accurate cross elasticity value.