1. Assume there are three markets: A: Wool; B: Synthetic Fiber; C: Business Travel. Assume we are in the years after the introduction of synthetic fibers. Using demand and supply analysis explain what happens in the SHORT RUN in all three markets and why?
2.Assume a monopolist with the following:
a. Qd = 100 – 10p
b. TC = 1 + 2Q
Find the following:
Price at profit max
Quantity at profit max
TR at profit max
TC at profit max
Profit
1. To analyze the short-run effects in each market (Wool, Synthetic Fiber, and Business Travel) after the introduction of synthetic fibers, we need to consider demand and supply conditions.
In the Wool market:
- Demand for wool will likely decrease as consumers shift their preferences towards synthetic fibers, which are generally cheaper.
- This decrease in demand will lead to a leftward shift of the demand curve for wool.
- As a result, the equilibrium price and quantity of wool will decrease in the short run.
- Producers of wool will experience a decrease in revenue due to the lower price and quantity sold.
- In the short run, wool producers might struggle to adjust their production levels and may experience losses.
In the Synthetic Fiber market:
- Demand for synthetic fibers will increase as consumers shift their preferences towards these cheaper alternatives.
- This increase in demand will lead to a rightward shift of the demand curve for synthetic fibers.
- As a result, the equilibrium price and quantity of synthetic fibers will increase in the short run.
- Producers of synthetic fibers will experience an increase in revenue due to the higher price and quantity sold.
- In the short run, synthetic fiber producers will likely enjoy higher profits and may invest in expanding their production capacity.
In the Business Travel market:
- The introduction of synthetic fibers may not have a direct impact on the demand for business travel.
- However, as synthetic fibers are generally cheaper, businesses might choose to reduce travel expenses by opting for synthetic fiber products or alternatives to business travel.
- This could lead to a decrease in demand for business travel services in the short run.
- As a result, the equilibrium price and quantity of business travel might decrease in the short run.
- Providers of business travel services will experience a decrease in revenue due to the lower price and quantity sold.
2. To find the price, quantity, total revenue, total cost, and profit at profit maximization for a monopolist with the given demand and cost functions, we can use the following steps:
a. Profit maximization occurs when marginal revenue (MR) equals marginal cost (MC).
- MR can be found by taking the derivative of total revenue (TR) with respect to quantity (Q).
- TR = Q * p (p is the price)
- MR = d(TR)/dQ = p + Q * dp/dQ (since p depends on Q)
b. To find the marginal cost (MC), take the derivative of total cost (TC) with respect to quantity (Q).
- TC = 1 + 2Q
- MC = d(TC)/dQ = d(1 + 2Q)/dQ = 2
c. Set MR equal to MC and solve for price and quantity to find the values at profit maximization:
- p + Q * dp/dQ = 2
d. Use the demand function (Qd = 100 - 10p) to substitute for Q in the MR equation:
- 100 - 10p + p * dp/dQ = 2
e. Solve the equation for p and substitute the value back into the demand function to find Q:
- 100 - 10(Price at profit max) + (Price at profit max) * dp/dQ = 2
- Solve for Price at profit max and substitute the value back into the demand function to find Quantity at profit max.
f. Calculate TR at profit max by multiplying Price at profit max by Quantity at profit max.
g. Calculate TC at profit max by substituting Quantity at profit max into the TC equation.
h. Calculate Profit by subtracting TC at profit max from TR at profit max.
By following these steps, you should be able to find the Price at profit max, Quantity at profit max, TR at profit max, TC at profit max, and Profit for the monopolist.