__Samples__

We have successfully solved thousands of problems for clients. Here we show a few samples of how our work looks like:

__Problem
1__

A perfectly competitive firm has total revenue and total cost curves given by:

TR = 100Q

TC = 5,000 + 2Q + 0.2 Q^{2}

a. Find the profit-maximizing output for this firm.

b. What profit does the firm make?

**Answer: **The profit function is given by

We differentiate to get:

The maximum profit is

The profit function is shown below:

__Problem 2__:

Assume that the demand
curve for bicycles in

.

a) What is the choke price? What is the slope of the demand curve? What is the slope of the supply curve?

**Answer: **In order to find the
choke price we solve:

The slope of the demand curve is , and the slope of the supply curve is .

b) Graph the supply and demand curves for the market of bicycles in NYC during the Fall.

**Answer: **We have the following graph:

c)
What
is the equilibrium price and quantity in the market for bicycles in

**Answer: **By intersecting the demand and supply curve
we get:

The equilibrium quantity is computed as

d) Fall has started in NYC. Unexpectedly, the weather turns out to be quite warm. Happy New Yorkers decide to spend more time biking around. As result, the original demand curve for bicycles in the Fall increases by 4 bicycles at every price. What is the new demand curve? Show it in the graph in (a).

**Answer: **The new demand is

In the new graph we have

e) What is the new equilibrium price and quantity?

**Answer: **Now we solve:

The new equilibrium quantity is

f) Why doesn't the new equilibrium quantity you found in (e) also increase by 4 bicycles? Briefly explain in words.

**Answer: **The new
equilibrium will not be obtained in general by adding the amounts of units that
demand was shifted, because it also depends on the interaction with the supply
curve.

**Topics**

We can help with the following topics:

- Economics Models
- Demand and Supply curves. Equilibrium
- Taxes
- Elasticity
- Utility Function
- Constrained Consumer choice
- Labor Supply
- Short and long run Production
- Marginal Product
- Isoquants
- Returns to Scale
- Short and long run costs
- Profit Maximization
- Welfare
- Monopoly. Market power
- Oligopoly. Stackelberg model
- Price Discrimination
- Game Theory. Nash equilibrium
- Managerial Economics

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