Question

Suppose there are two demand curves (e.g two different sets of consumers) for a particular product (two distinct markets that can be segmented-so somehow the consumers in one market cannot buy in the other market). The two demand curves are given by the following equations:

Q₁=200−P₁ (group 1)
Q₂=100−2P₂(group2)
This product is produced in one factory and has a constant MC=$40.
a. Solve for the inverse demand curve for group 1 and then graph the inverse demand curve with P on the vertical and Q on the horizontal axis. In graphing this, I expect you to solve for the actual values of the P axis and Q axis intercepts for both demand curves. Also indicate the numerical value of the slope for the curve. Repeat the same steps for the second group. Calculate profits for this firm.
b. Calculate MR for each group above and graph on the graphs in part a.
c. Find the profit maximizing output and price in each market. Label the profit maximizing price and quantity for each graph in part.
d. What are the price elasticities of demand at the profit maximizing quantities (and prices) that you found in part
e. Using the concept of elasticity of demand, explain why the price is higher in one market versus the other.

Answer 1

To solve for the inverse demand curves, rearrange the equations to solve for price. Calculate the intercepts and slopes of the demand curves. To calculate profits, set MR equal to MC and find the equilibrium quantity and price in each market.

Step-by-step explanation:

To solve for the inverse demand curve for group 1, we rearrange the equation Q₁ = 200 - P₁ to solve for P₁. We get P₁ = 200 - Q₁. The intercepts for the demand curve are P₁ = 200 and Q₁ = 0. The slope of the curve is -1.

Similarly, for group 2, we rearrange the equation Q₂ = 100 - 2P₂ to solve for P₂. We get P₂ = (100 - Q₂)/2. The intercepts for the demand curve are P₂ = 50 and Q₂ = 0. The slope of the curve is -0.5.

To calculate profits for the firm, we need to find the equilibrium quantity and price in each market. This can be done by setting MR (marginal revenue) equal to MC (marginal cost) for each group. To find MR, we take the derivative of the demand equation with respect to quantity.