Economics and Industry Analysis (Microeconomics)

Problem 1

Suppose the demand curve for milk is described by the equation Q_D = 600 - 100 P and the supply curve is described by the equation Q_S = -150 + 150 P, where P is the price in dollars per litre, Q_D is the quantity demanded in millions of litres per year and Q_S is the quantity supplied in millions of litres per year.

a. Graph the supply and demand curves. Calculate (algebraically) the equilibrium price and quantity and show them in the graph.

b. Suppose a hormone is introduced that allows dairy farmers to offer 125 million more litres of milk per year at each price. Show the impact in your graph and determine the new equilibrium price and quantity.

c. After the hormone is introduced, the government sets the price of milk at $3 a litre. Show the imposition of this regulation in your diagram. What is the quantity demanded and supplied now?

d. The hormone remains in place, but the price regulation is removed and, instead, the government imposes a tax of $1 per litre on dairy farmers. Show the tax in your diagram. What price will the milk farmers get? What price will consumers pay? What is the total amount of government tax revenue?

Problem 2

A textile fibre is traded in a competitive world market, and the world price is $9.00 per pound. Unlimited quantities are available for import into Canada at that price. The Canadian domestic supply is described by the equation Q = 0.67 P, and the Canadian domestic demand is described by the equation Q = 40 - 2 P.

a) Plot the supply and demand curves

b) At the price of $9.00, what is the price elasticity of demand? What is the price elasticity of demand at $12.00?

c) What is the price elasticity of supply at $9.00? At $12.00?

d) In a free market (no import tariffs or quotas), what will be the Canadian price and the level of fibre imports? Illustrate the outcome in a diagram.

Problem 3

A manufacturer of computer workstations gathered average monthly sales figures from 56 branch offices and dealerships across the country (all data were collected at the same date) and estimated the following demand for its product:

Q = 15,000 - 2.80 P + 150 A + 0.3 PPC + 0.35 Pm + 0.2 Pc ,
(5,234) (1.29) (175) (0.12) (0.17) (0.13)
R-squared = 0.68 SEE = 786 F = 21.25
where

Q = quantity;

P = price of basic model (=7,000);

A = advertising expenditures, in thousands (=52);

PPC = average price of a personal computer (=4,000);

Pm = average price of a minicomputer (=15,000);

Pc = average price of a leading competitor's workstation (=8,000);

The figures in brackets below the coefficients are standard errors.

NOTE:

From your statistics course, you will recall that a simple regression of quantity on price (Q= a - bP) gives you information about the demand curve. If you tried to determine from this demand curve by how much the quantity demanded changes in response to a price change, you could make a serious error if there was both a change in price and a shift in the demand curve. The procedure of running a multiple regression amounts to recognizing that the "other things" (in this case, advertising, the price of personal computers, the price of minicomputers, and the price of a competing workstation product) might have changed, i.e. the demand curve might have shifted. The result is an estimate of a demand function. Each coefficient represents the change in quantity demanded resulting from a unit change in the variable in question, holding all other variables constant (i.e. multiple regression "takes care" of the various shifts in the demand curve).

a). Compute the elasticities for each of the variables. Discuss the relative impact that each variable has on demand. What implications do these calculations have for the firm's marketing and pricing policies?

b) Discuss the statistical significance of each coefficient. Explain whether a one-tail or two-tail test is required. Suppose a manager evaluating these results suggests that interest rates and the performance of computer workstations (typically measured in millions of instructions per second, or MIPS) are important determinants of the demand for workstations and must therefore be included in the study. How would you respond to this suggestion? Elaborate. (Hint: Recall that all information pertains to a single month and was collected at the same date).

Problem 4

Howard is a large cotton farmer. The land and machinery he owns has a current market value of $4,000,000. He owes his local bank $3,000,000. Last year Howard sold $5,000,000 worth of cotton. His variable operating costs were $4,500,000; accounting depreciation was $40,000, although the actual decline in the value of Howard's machinery was $60,000. He paid himself a salary of $50,000 (this was not included in the variable operating costs given above). Interest on bank loan was $400,000. If Howard worked for another farmer or for a local manufacturer, his annual income would be about $30,000. If he decided to sell the farm, the proceeds would be invested to earn 10% annually. Ignore all taxes

a) Calculate Howard's accounting profit

b) Calculate his economic profit

c) Which of the costs are explicit and which are implicit?

d) Would you recommend that he sell the farm? What other considerations might be relevant?

Problem 5

The LTP company manufactures lawn and patio furniture. Sales are highly seasonal, with 80 percent concentrated in the January-June period. Production is normally concentrated in the September-May period. Approximately 75% of the hourly workforce (unskilled and semiskilled workers) is laid off or takes its paid vacation time during the June-August period of reduced output. The remainder of the workforce, consisting of salaried plant management, maintenance and clerical staff are retained during this slow period.

LTP planned to produce and sell 500,000 of these chairs during the coming year at a projected selling price of $7.15 per chair. The cost per unit was estimated as follows:
Direct labour $2.25
Materials 2.30
Plant overhead* 1.15
Administrative and selling expenses* .80
TOTAL 6.50
*These costs are allocated to each unit of output based on the projected annual production of 500,000 chairs.

In May, LTP received an inquiry from a department store chain concerning the possible purchase of folding chairs for delivery in August. The chain indicated that it would place an order for 30,000 chairs if the price did not exceed $5.50 each (plus shipping). The chairs could be produced during the slow period using the firm's existing equipment and workforce. No overtime wages would have to be paid, and adequate materials are on hand (or could be purchased at prevailing market prices) to complete the order.

LTP management is considering whether to accept the order.

a) Calculate the incremental (marginal) cost per chair to LTP of accepting the order.

b) What assumptions did you make in calculating the incremental costs in (a)? What additional information would be helpful?

c) Should LTP accept the order?

d) What additional considerations might lead LTP to reject the order?

Problem 6

Consider a firm with plants for relining brake shoes in the U.S., Canada, and Mexico. All output is shipped to a distribution centre in Kansas, and shipping costs from the three plants to the centre do not differ significantly. Canadian and Mexican domestic sales are small compared with sales in the U.S.

If the plants have the marginal costs given in the table below, what is the optimal allocation of total output of 14,000 units per week among the three plants?

Explain briefly your reasoning.

(Note: No complicated calculations are required. The allocation of output should be such that at the margin, the costs in each plant are approximately the same).

Problem 7

John's Lawn Mowing Service is a small business that acts as a price taker. The prevailing market price of lawn mowing is $20 per acre. Although John can use the family mower for free, he has other costs given by

TC = 0.1 Q2 + 10 Q + 50

and

MC = 0.2 Q + 10,

where Q = the number of acres John has chosen to mow in a week.

a) How many acres should John choose to mow in order to maximize profits?

b) Calculate John's maximum weekly profit.

Suppose John's father decides to charge John for the use of the family lawn mower.

c) If the lawn mower fee is set at $100 per week, what will be

- the profit-maximizing number of acres John chooses to mow?

- John's profits?

d) Suppose next that John's father removes the $100 weekly fee and instead imposes a charge of $2 per acre for the use of the family mower, what will be
- John's marginal cost function?

- the profit-maximizing number of acres John chooses to mow?

- John's profits?

e) The $2 per-acre charge remains in place, and the government is thinking of instituting a subsidy for John's business. Two plans are under consideration: (1) a flat grant of $200 per week to John; and (2) a grant of $4 per acre mowed.

- Which of the two plans will John prefer?

- What would be the cost of plan (2) to government?

f) Suppose now that the subsidy - either plan (1) or plan (2) applies to all lawn mowing service businesses. Without reference to specific numbers, use a diagram showing the long-run impact of the subsidy
- on the market price of lawn mowing
- on the amount of lawn mowing in total and per firm.

Problem 8

The ice cream industry is perfectly competitive. Each firm must hire an operations manager. There exist only 50 extraordinarily talented managers in the market yet an unlimited supply of average talented managers. Yet (despite reality!) they are all paid $200,000 per year.

- The long-run total cost (in thousands of dollars) faced by firms faced by firms with extraordinarily talented managers is given by LTCE(Q) = 200 + Q2 where Q is measured in thousands of 5-gallon tubs of ice cream. The corresponding marginal cost function is given by LMCE(Q) = 2Q and the corresponding long-run average total cost is LATCE(Q) = 200/Q + Q.

- The long-run total cost (in thousands of dollars) faced by firms with average talented managers is given by LTCA(Q) = 200 + 2Q2. The corresponding marginal cost function is given by LMCA(Q) = 4Q and the corresponding long-run average total cost is LATCA(Q) = 200/Q + 2Q.

a). Derive the supply curve of a firm with an extraordinarily talented manager.

b). Derive the supply curve of a firm with an average talented manager.

c). The minimum LATCA(Q) is equal to $40, achieved when those firms produce 10 units of output. The minimum LATCE(Q) is equal to $28.28, achieved when those firms produce 14 units of output. Explain why, given only that information, it is not possible to determine the long-run equilibrium price of 5-gallon tubs of ice cream.

d). Refer to part (c). Suppose that you know that the market demand for ice cream I given by QD(P) = 8,000 - 100P. Explain why, in the long run, that demand will not be filled solely by firms with extraordinarily talented managers. (Hint: Derive the industry supply of firms with extraordinarily talented managers and then use the demand curve to determine the equilibrium price. Can that price persist in the long run?)

e). Refer to part (d). You explained why the supply side of the market will consist of both types of firms. What will the long run equilibrium price of ice cream be?

f). At the price you determine in part (e), all 50 firms with extraordinarily talented managers will find remaining in the industry worthwhile. How many firms with average talented managers will also remain in the industry?

g). At the price you determined in part (e),how much profit will a firm with an average talentedmanager earn?

h). At the price you determined in part (e), how much profit will a firm with an extraordinarily talented manager earn? How much economic rent will that extraordinarily talented manager generate for her firm?