**Economic Issues – BUSA 5203 – OC – HW 1 (Ch1-Ch2)**

**Directions:** Answer all the following questions. Make sure to show all work and any formulas or graphs needed in the solution. All the solutions should be put in your solutions document. You may modify this word document and put all solutions on it. Make sure to start each question on a new page

** **

**Questions:**

**Question 1 – Present and Future Values**

- Suppose that you invest $5000 each year for 5 years and that you expect to earn an interest rate of 5.5%? How much money should you have in 15 years? Show all work.

- Fred is considering the purchase of a lease that will allow him to operate a restaurant at the local airport for a period of five years. The lease will cost $32,000
along with__annually__of 4,000. Fred anticipates__monthly operation costs__of $15,000. Calculate the PV of the expected profits of the investment? Assume i = 0.067.__monthly revenues__

**Question 2: Marginal Analysis**

- Given the following chart explain what the optimal Q is. Use both the total and marginal approach to verify your result.

Q |
TB (Q) |
TC (Q) |

0 | 0 | 0 |

1 | 25 | 15 |

2 | 55 | 25 |

3 | 95 | 45 |

4 | 130 | 75 |

5 | 165 | 110 |

6 | 195 | 155 |

__*note that part a and part b are different questions.__

- Suppose you are given that fact that TB(Q) = 100 + 20Q – 2Q
^{2 },TC(Q) = 20 +2Q + Q^{2} - Find MB and MC. Show all your work.
- Write the expression for NB and MNB.

iii. Find the optimal Q and calculate the NB associated with that Q. Verify that it is indeed the optimal NB using MB and MC.

**Question 3 – Supply and Demand**

Assume that the demand and the supply in a market are represented by the following equations:

_{ }

Qd = 210 – 3P

Qs = 2P -40

(i) Compute equilibrium P and Q:

(ii) Illustrate your results in a graph (make sure it is labeled) noting all important points and axes as well as max purchase price and min selling price.

(iii) Find CS, PS and TS for the market. What do CS and PS represent?

**Question 4 – Supply/Demand and Elasticity**

Assume that the demand for product *X* is represented by the following equation:

- i) Which of the products
*Y*and*Z*is a substitute to*X*in consumption? Which is a

complement? Explain.

- ii) If you are told that Py = 25 and Pz = 50, find the simple linear demand equation and graph it.

iii) Find the elasticity of demand if you are told that Px = 30. Is good X inelastic/elastic? Explain.

**Question 5 – Supply/Demand and Elasticity**

** **

Sometimes firms conduct experiments where they temporarily change prices (this may be done with selective coupons and other discounting methods) to see how the consumer responds to a price change. Let’s assume that our firm charges $10 per unit of output and on average has 600 units sold per day. However, for the last week the firm offered a $1 discount and charged only $9 per unit of output. During the week of the discount the firm observed that the average daily sales were 700 units.

(i) Given the price and quantity information, calculate the Elasticity of Demand for the product.

(ii) What type of good/service is this (inelastic, elastic, etc.)? Explain.

(iii) Interpret your elasticity calculation using a 1% change in P.

(iv) Is the price change that the firm used a good idea? Explain in terms of total revenue.

**Bonus: Part (v) and (vi) are considered bonus. **

(v) If we operate under the assumption of *ceteris paribus*, what is the best linear representation of the demand faced by the firm [please provide the equation for the demand in terms of *Q* = *f*(*P*). **Hint:** This is just solving for the equation of the line…so solve for slope and intercept.

Recall that to get the equation of a line we can choose one point and note:

(Y – Y1) = M(X – X1) à in this case your point would be (X1, Y1) à (P,Q) where M =

(vi) If we continue to operate under the assumption that the demand is linear, what prediction can you make about the firm’s level of sales at the price of $8? Use your solution to part (v) to predict this.