Managerial Economics

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Attribute YAttribute X

Figure 1: ProductAttributes Model

1.2 Are any of the products priced out of the market, in the sense that no rational consumer would buy it? Which one? What price adjustment would make that product potentially competitive? Explain and show your analysis on Figure 1 above.

(Note: For Figure 1 we have provided some graphing shapes on the side that you may choose to use for your graphical analysis throughout this problem. You are still responsible for using them appropriately in terms of length, orientation, number of use etc. Alternatively, you may submit a scanned PDF of all or part of the homework assignment and/or the final exam.)

QUESTION 2 (Demand Analysis):

Suppose that the demand for a product X has been estimated to be:

Qx = 400 + 0.002I + 8Z – 5Py – 20Px

Where Qx is the quantity demanded for the product X, Px is the price of product X, Py is the price of a related product Y, I is the level of income, and Z is some other variable that affects the demand for product X.

Current values of the variables are: I = 10,000; Z = 150; Py = 50; Px = 50

2.1 Calculate the quantity of sales of Qx at the current values of the other variables.

Qx = _____________________________

Show work here:

2.2 Calculate the own-price elasticity of demand, income elasticity of demand, and cross-price elasticity of demand with product Y at the current values of the variables.

Own-price elasticity

Income elasticity

Cross price elasticity

2.3 Construct the demand, inverse demand, and marginal revenue equations for product X. Also find the revenue maximizing quantity and price. Show all work. (Calculate the coefficients in Inverse demand and Marginal revenue equations up to 2 decimal points.)

Demand Curve Equation: Qx = ___________________________

Inverse Demand Curve Equation: Px = ___________________________

Marginal Revenue Equation: MRx = ___________________________

Revenue Maximizing Quantity__________________

Revenue Maximizing Price _____________________

Show work here:

2.4 Assuming marginal cost equals 20, what is the profit-maximizing price and quantity for product X?

P* = _____________________ Q* = _____________________________

Show work here:

2.5 What is the own-price elasticity of demand at the profit-maximizing price and quantity? Check your answer to 2.4 by using the optimal markup pricing formula (that relates optimal price, elasticity at optimal price and quantity, and marginal cost at the optimal quantity). Show your calculation.

Elasticity at P*, Q* = _________________________(Calculate up to 5 decimal points)

Optimal Markup Pricing:

QUESTION 3 (Costs of Production):

3.1 Given the total cost function: C = 1000 + 25Q + 0.05Q2 and associated MC = 25 + 0.1Q

Calculate each of the following values at Q = 10:

Total Fixed Cost

Total Variable Cost

Average Fixed Cost

Average Variable Cost

Average Total Cost

Marginal Cost

3.2 Fill in the blanks in the table below, reflecting short-run costs of producing a product:

(Note: This problem is independent of problem 3.1 and the table below does NOT use the cost function shown in 3.1)

Q	Total Cost	Total FC	Total VC	ATC	AFC	AVC	MC
0
1				1050
2		1000				60
3							75

3.3 Fill in the blanks using your knowledge of various short run and long run characteristics of cost. (Note: Again, this problem is independent of problems 3.1 and 3.2)

Hubert has opened a bakery that makes cupcakes. For his first year of operation, he operates the bakery out of his home kitchen. He finds that when he pays his brother to help him, he is able to produce cupcakes at lower ATC than when he works alone. An economic reason for the lower ATC is likely to be

_______________________________________________

By his second year of operation, Hubert’s cumulative output has increased. He finds that his ATC for the second year is lower than it was in his first year of operation, whether he works alone or whether he hires his brother to help him. A likely economic reason for his lower ATC in Year 2 is

______________________________________________.

In his third year of operation, Hubert leases space in a commercial kitchen, where he has access to large ovens, large mixers, and other such equipment. Hubert finds that his ATC is even lower than before. A new reason for the lower ATC might be

___________________________________________________.

QUESTION 4 (Value Pricing):

Meow-Bow Pet Transport Company operates a pet airline service between New York and several major cities. All of its business consists of shipping dogs and cats. The inverse demand functions for the two market segments are:

For dog transport:

Pd = 110 – 0.2Qd

For cat transport

Pc = 70 – 0.1Qc

Where, Qd = number of dogs transported per day and

Qc = number of cats transported per day

Suppose that the average variable cost as well as marginal cost of pet transport for MBPT Company is $10 and is constant over the range of output under consideration.

4.1 What are the profit-maximizing prices and number of pets carried for each of the two types of pets, assuming that MBPT is able to practice third degree price discrimination for the two markets?

Dog transport Cat transport

Pd =____________________________ Pc QUOTE =______________________________

Qd QUOTE = ____________________________ Qc QUOTE = ______________________________

Show your work here:

4.2 What is MBPT’s per unit contribution from each of the two markets?

Per Unit Contribution from dog transportation = __________________________________

Per Unit Contribution from cat transportation = __________________________________

Show your work here:

QUESTION 5 (Assessing Competitor Response)

Two players face the following possible payoffs. If

Row Player plays Tough and Column Player plays Tough, both have profits of 100

RP plays Nice and CP plays Nice both have profits of 200

RP plays Nice and CP plays Tough, RP gets 0 and CP gets 250

RP plays Tough and CP plays Nice, RP gets 250 and CP gets 0.

Arrange the payoffs described above in the payoff matrix below.

5.1 Does RP have a dominant strategy? Does CP have a dominant strategy? If so, what is it? Is there any Nash equilibrium in this game? Explain clearly.

5.2 Suppose the game is, instead, a repeated game that will repeat as far into the future as either player can imagine, with no end point in sight.  Use the standard calculation method to illustrate the answer to the following question - If the players engage in tit-for-tat and each player has a 10% discount factor, is the Nash Equilibrium possibly going to be different from the one-shot game in part 5.1 above?

5.3 (Note: This part of the question is independent from the information in parts 5.1 and 5.2). Two Firms ABC and XYZ are the only two competitors in a certain market. XYZ has recently introduced a new variety of product in the market at a high price and (as the only seller) is currently earning a profit of $300 million from this new product. If XYZ (as the only seller) sells its product at a low price, its profit would be $200 million. ABC does not yet have a product of this new variety to compete directly with XYZ’s new product and is considering introducing such a new product. If ABC does introduce the new product, XYZ could adopt one of two strategies: (1) XYZ could continue to charge the high price, and ABC and XYZ would earn $200 million and $275 million, respectively, or (2) XYZ could charge a low price, in which case ABC and XYZ would each earn $10 million and $100 million respectively. Should ABC introduce the new product? Why or why not?

Use a game tree to illustrate the profit possibilities. Remember to label all important parts of the diagram. Mark on the game tree the equilibrium path using the method of backward induction (i.e., roll back technique or looking forward and reasoning backward) learned in the course. What will be the payoffs to each firm?

QUESTION 6 (Externalities and Efficiency)

6.1 Using the graph below depict a demand-supply graph for the market for paper and paper products. The production of paper and paper products creates pollution which affects human health as well as the eco-system. Show the market equilibrium for this market in general, with no government intervention. Be sure to identify any externalities that make social benefit or cost different from private benefit or cost. Is the market efficient? Explain. (Remember to label the axes, curves and all important points.)

6.2 Clearly show on your graph the effect of a per unit production tax on the final equilibrium price and quantity in this market. Again, make sure to label all important curves and points.

Column Player

Row Player