10- Calculate the consumer surplus and producer surplus for the following demand an supply equations: Demand: P=100-2Q Supply: P=20+3Q Assume the market is in equilibrium. (10 points)

To calculate the consumer surplus we first need to find the equilibrium price and quantity. The equilibrium occurs where the demand and supply equations are equal, i.e., where .Setting the demand equation equal to the supply equation: Solving for : Now, substitute into either the demand or supply equation to find the equilibrium price : The equilibrium price is Q = 16 \text{Consumer Surplus} = \frac{1}{2} \times (\text{Base}) \times (\text{Height}) Q = 16 Q = 0 \text{Height} = 100 - 68 = 32 \text{Consumer Surplus} = \frac{1}{2} \times 16 \times 32 = 256 \text{Producer Surplus} = \frac{1}{2} \times (\text{Base}) \times (\text{Height}) Q = 16 Q = 0 \text{Height} = 68 - 20 = 48 \text{Producer Surplus} = \frac{1}{2} \times 16 \times 48 = 384 256 384$.