Intermediate Microeconomics Assignment -
Part A -
Q1. Market Demand and Elasticities - Consider the demand for an a Cadillac Escalade. Suppose that the demand is Qd = 500 - 3P + 3PKIA - 2PRW, where P is the price of an Escalade (in thousands of dollars), PKIA is the price of a Kia Sorrento (in thousands of dollars), and PRW is the price of the platinum-plated wheel rims people put on Escalades. Assume that supply is given by Qs = 100 + 7P. Assume PKIA = 40 and PRW = 10.
a) What is the equilibrium price and quantity for the Escalade?
b) What are the coefficients for the price elasticity of demand and supply the Escalade?
c) What are the cross-price elasticities on the demand for big SUVs with: 1) the price of the Kia Sorrento and 2) platinum-plated wheel rims? How do you know for sure if they are complements or substitutes?
d) What if the government wants to impose a tax on big SUVs like an Escalade because they get low miles per gallon but not on small SUVs like the Kia Sorrento? How much will the price increase if a tax of 10 (in thousands of dollars) is placed on the production of each Escalade?
Q2. Price Floor - What are the effects in the market for sugar when the government agrees to pay U.S. sugar farmers the difference between $5 per pound of sugar and the price U.S. consumers are willing to pay for a pound of sugar? This is known as a deficiency payment system. Using the letters depicted in the graph below, determine social welfare with a market outcome and a price floor outcome. Identify the deadweight loss resulting from the government's policy.
Mathematical Calculations:
a) Calculate total Social Welfare under market conditions.
b) Calculate producer surplus with the price floor.
c) Calculate the deadweight loss.
Q3. Indifference Curves -
a) Explain why indifference curves cannot intersect.
b) (True or False) Indifference curves will be more convex for combinations of t-shirts and hamburgers than combinations of hot-dogs and hamburgers. Explain.
Q4. Consumer Choice Optimum -
a) Marco consumes only bananas and t-shirts. At his current consumption bundle, he is spending all his income and his marginal utility from the last banana he consumed is 5 utils and from his last t-shirt is 20 utils. Each banana costs $2 and each t-shirt costs $10. Is Marco maximizing his utility? Explain. Draw a graph of the consumer choice model for Marco showing his current utility level and whether he can improve his situation. (Place Bananas on the x-axis)
b) Using the budget constraint and optimum as the graph above, now using the graph below show what happens when the price of bananas falls to $1 and assume that Bananas are inferior goods for Marco. Show the substitution and income effects.
Q5. Consumer Choice Theory - Mason likes yogurt and kale. The price of yogurt $1each and the price of kale $2 each. Mason has a budget equal to $100 and a utility function equal to U = 100Y - 0.5Y2 + 120K - 0.5K2 - YK.
a) Does Mason consider yogurt and kale to be complements or substitutes? How can you tell from the utility function?
b) Use a Lagrangian multiplier (calculus) to solve Mason's constrained optimization problem to find Y* and K*, his optimal consumption of both goods.
c) Illustrate your answer on a graph with indifference curves, labeling your graph with Y*, K*, and Mason's optimal utility U* on the indifference curve.
d) Mathematically prove that the Utility Maximizing Rule (i.e., tangency) holds for Mason at Y* and K*.
Q7. Uncertainty and Insurance - Assume that you own an office building in the Bay Area. Your utility is given by U = V1/2, where V is the value of the office building. Suppose all of your wealth is invested in the value of the office building. The probability of a strong earthquake occurring this year is 1%. If it does occur the value of the building will fall from $9,000,000 to $1,000,000.
a) Given the chances of an earthquake, what is the expected value of the building?
b) If you buy enough insurance to guarantee yourself wealth equal to the expected value. How much insurance coverage will you buy and what will be the "fair insurance" premium for such coverage?
c) What is your expected utility without insurance?
d) What is the reservation price (a.k.a., highest premium you will pay) for the insurance coverage you would have bought in response to (c) above?
Q8. Uncertainty and Investing -
The graph above represents Jed's utility function for different levels of wealth. Suppose Jed starts with $40,000 of wealth and corresponding utility of 150. Jed is presented with an investment opportunity that will either make his wealth go up to $80,000 or go down to $30,000. In other words, the investment will either make him $40,000 in profit or he will lose $10,000. Suppose there is a 25% chance that investment will go bad and 75% it will go well.
a) Based upon the above diagram how does Jed view risk?
b) What does the point on the chord represent? Explain.
c) Will Jed make the investment? Explain.
d) If you offered Jed $14,000 in cash or the investment opportunity, which one would he take and why?
Q9. Departures from Rationality - Identify these behavioral anomalies, describe why they violate the basic assumptions of the standard economics model, and give a real-world example the effect.
a) Halo Effect:
b) Sunk Cost Fallacy:
Q10. Multiple Choice - One correct answer
1. Before satiation, the principle of diminishing marginal utility will cause, any increase in consumption of a good to
a) lowers total utility.
b) produces negative marginal utility.
c) reduce marginal utility and, therefore, total utility.
d) reduce marginal utility, but increase total utility.
2. The phenomenon of the backward-bending market supply curve for labor
a) indicates an increasing desire for leisure as income rises.
b) reflects the scarcity of high-priced, highly skilled labor.
c) results from workers' general preference for leisure over work.
d) results from the effect of the decrease in the cost of leisure as wage rates rise.
3. If the income consumption curve is positively sloped. The Engle's curve will be:
a) Positively sloped for both goods.
b) Negatively sloped for both goods.
c) Positively sloped for the good on the y-axis and negatively sloped for the good on the x-axis
d) Positively sloped for the good on the x-axis and negatively sloped for the good on the y-axis
4. Which is true: When a country goes from free trade to imposing a tariff a portion of the deadweight loss is the result of:
a) How the government spends the tax revenues.
b) The loss of consumer surplus that would have been enjoyed by consumers who now choose to not purchase the product at the higher price.
c) The loss of consumer surplus by consumers who purchase the product at the higher price.
d) The transfer of welfare from consumers to producers.
5. Suppose the demand curve is more inelastic than the supply curve. A tax imposed on suppliers will cause:
a) a larger loss of consumer surplus than producer surplus.
b) an equal loss of producer surplus and consumer surplus.
c) a larger loss of producer surplus than consumer surplus.
d) price to increase by less than 50% of the tax.
6. Moving down a negatively sloped linear demand curve:
a) the price elasticity of demand remains constant.
b) the price elasticity of demand becomes more inelastic.
c) the price elasticity of demand becomes more elastic.
d) the price elasticity of demand remains unit elastic.
7. Mia initially consumes 10 tacos per month. Then the price of tacos decreases by 10 percent. The substitution effect is +5 and the total effect is +2, such that after the price decrease Mia consumes 12 tacos. Which two of the following are true for Mia?
a) Tacos are Giffen goods.
b) For tacos the income elasticity of demand is greater than 0.
c) Price elasticity of demand for tacos is inelastic.
d) Price elasticity of demand for tacos is elastic.
e) Tacos are inferior goods with respect to a price decrease.
f) Tacos are normal goods with respect to a price decrease.
8. Assume that Bruno's utility is given by U = Y1/2. Calculate Bruno's expected utility from a gamble in which Bruno will get $100 with probability 0.9 and $0 with probability 0.1? Would is the certainty ("guaranteed money") equivalent of this gamble?
a) $90
b) $81
c) $84
d) $75
9. In the above, problem how much is Bruno's risk premium?
a) $10
b) $9
c) $8
d) $7
Part B -
Q1) Short Run Cost Curves - The curves below reflect information about the cost structure of a firm. Use the figure to answer the following questions:
a. Identify by letter which of the curves above is average total cost _B__, average fixed cost __D__, average variable cost __C__, and marginal cost__A__.
b. Describe the relationship between curves B and curve C.
c. Describe the relationship between curves A and B.
Q2) Long-Run Production and Profit Maximization - Dominic's Manure Co. is a producer of fertilizer. There are two inputs that make the manure fertilizer: Cows (C) and Hay (H). Cows cost $4/pound and Hay costs $2/pound. The production function for Dominic's Manure Co. is given by q = 24C - 0.5C2 + 18H - 0.5H2. Currently the company has an expenditure constraint (budget) equal to $52.
a) Derive the profit-maximizing level of Cows (C*) and Hay (H*) for Dominic's Manure Co. subject to their budget constraint.
b) Show that the "profit maximizing rule" (a.k.a. the MRTS is equal to the input price ratio) at C* and H*.
c) Find q* with the optimum level of inputs.
d) Suppose the market price for manure is $10/sack. How much is profit at q*?
Q3) Production and Costs - Briefly describe the following terms by explaining when, how or why they may occur.
a) The law of diminishing returns:
b) Diseconomies of scale:
c) Constant Cost Industry:
Q4) Perfect Competition - Bruno grows artichokes. The price of artichokes is $50/box. His cost function for artichokes is TC = 400 + 5q + 0.25q2. (Show work)
a) Based on the current price how many boxes of artichokes should Bruno produce?
b) How much is his total profit?
c) In the long-run, how many boxes will Bruno produce and what will be the price of each box?
Find where MC=ATC
Q5) Natural Monopoly - Suppose that PG&E is a natural monopoly. PG&E faces the following inverse demand curve for monthly demand for gas: P=260- ¼ Q. Suppose its marginal and average variable costs are a constant $10 per kilowatt hour.
a) Find the profit maximizing quantity and price if this natural monopolist was not regulated.
b) Draw a graph for the monopolist, showing the demand curve, the marginal revenue curve, and the profit maximizing output and price.
c) Now suppose that the natural monopolist is regulated as to price and quantity. Assume that average fixed costs at Q(reg) is $30. Find Q(reg) and P(reg). Show your answers in the graph above.
Q6) Monopolistic Competition -
a) List four assumptions associated with monopolistically competitive markets.
b) In the long run, does a monopolistically competitive firm operate in the upward sloping section of its average total cost curve in the long run? (First draw the graph and then explain in words.)
Q7) Price Discrimination -
a) Demand for the latest book by Scott Turow is equal to Pd = 80 - 2qd among his die-hard fans, and equal to Pc = 39 - qc among his casual readers. The average and marginal cost of a paperback book is $5 and a hardback is $8. As the publisher of his books, what price will you charge for the hardback edition, and what price will you charge for the paperback edition that comes out six months later? Show your work.
b) Using the Lerner Index formula. Determine the price elasticity of demand in each market? Explain.
Q8) Oligopoly - Suppose that the Town of Pescadero has two suppliers of wood Big Creek Lumber, Inc. and Coastal Lumber, Inc. Assume that the wood is homogeneous and that the market demand for wood in the town is P = 250 - 2Q. Each firm has average and marginal costs equal to $10.
a) Cartel: If Big Creek and Coastal form a cartel how much will each produce and what will be the price? Calculate profits for each.
b) Cournot: What is the Cournot equilibrium outcome for this duopoly? What are equilibrium prices and quantities for each wood supplier? Calculate each firm's profits.
c) Bertrand: What is the Bertrand equilibrium outcome for this duopoly? What are equilibrium prices, quantities, and profits or each wood supplier?
In Bertrand with homogeneous goods P=MC.
d) Kinked Demand: If a firm believes it is facing a kinked demand curve, what assumptions does the firm make regarding its rival's reactions to its own price changes? If there is an increase in production costs (a leftward shift in marginal cost) does a firm facing a kinked demand curve increase its price? (Explain why or why not- you may draw a graph, but it is not necessary)
e) Game Theory: Suppose Burger King and McDonalds are considering how much money they should spend on advertising in the year 2016. They have two options, a large budget or a small one. Assume that advertising increases each restaurant's total revenues and total costs and, therefore, affects their profits. The restaurants face the following profits. Remember the upper right-hand numbers of each box are McDonald's profits and the lower right are Burger King's profits.
|
|
McDonalds
|
|
Small Budget
|
Large Budget
|
|
Burger King
|
Small Budget
|
$10,000
|
$18,000
|
|
$10,000
|
$5,000
|
|
Large Budget
|
$5,000
|
$8,000
|
|
$18,000
|
$8,000
|
a) Find the Nash Equilibrium.
b) Briefly explain why this outcome is an example of the prisoner's dilemma?
Q9) Multiple Choice:
a) ATC is given by:
1) The slope of the total cost curve.
2) The difference between AFC and AVC.
3) The slope of the ray from the origin to a point on the total cost curve.
4) The slope of the marginal cost curve.
b) In the long-run, if the MPK is twice the MPL and the rental rate is 1.5 times the wage, then:
1) The firm can increase its output while spending the same amount of money by increasing the amount of capital while reducing the amount of labor.
2) The firm can increase its output while spending the same amount of money by increasing the amount of labor while reducing the amount of capital.
3) The firm is experiencing constant returns to scale.
4) The firm can produce the same output at a lower cost by hiring more workers and renting less capital.
c) In perfect competition:
1) Economic profits are equal to accounting profits in the long-run.
2) Accounting profits can be greater than implicit costs in the short-run.
3) Economic profits can be greater than accounting profits in the short-run.
4) Implicit costs are zero in the long-run.
d) Firms in monopolistically competitive and perfect competition markets have in common:
1) a perfectly elastic demand curve
2) many potential buyers and sellers
3) market power
4) significant barriers to entry
e) Which is NOT correct? A copyright
1) lasts for a longer time than a patent
2) tends to increase price
3) creates a barrier to entry
4) must be approved by the government.
f) Which of the following statements regarding price discrimination is false?
1) Price elasticities are different among different types of consumers.
2) A perfect competitor can increase its profits by practicing price discrimination.
3) In order for a firm to be able to price discriminate it must be able separate its consumers into divisible groups.
4) A monopolist can increase its profits by practicing price discrimination.
g) A perfectly competitive firm has chosen its profit maximizing (loss minimizing) level of output. At this level of output, its price is $18, average variable cost is $15 and average total cost is $20. The firm
1) Should shut down immediately
2) Is making a profit of $5 per unit of output.
3) Is losing $25 per unit of output.
4) Should continue to produce in the short-run because the price exceeds the average variable cost.
h) Which of the following is NOT correct? A typical monopoly
1) Can earn economic profits in the long run.
2) Charges a price that has an inelastic price elasticity of demand.
3) Produces a quantity where marginal revenue is equal to marginal cost.
4) Charges a price on the elastic portion of the demand curve.
i) In the long run, a monopolistically competitive firm produces
1) Less than a monopolist
2) Equal to a perfect competitor
3) Where marginal cost is equal to price.
4) At a price that is above what a perfect competitor charges.
j) Which of the following two statements are true about market structures in LR equilibrium?
1) P = minimum AC for both perfect competition and monopolistic competition.
2) P > minimum AC for both Cournot competition and monopolistic competition.
3) Positive economic profits can exist in both Bertrand oligopoly with homogeneous products and Cournot oligopoly.
4) Zero economic profits exist in both Bertrand oligopoly with heterogeneous products and monopolistic competition.
5) Positive economic profits can exist in both Bertrand oligopoly with heterogeneous products and Cournot oligopoly.