Q1. You have an opportunity to invest in a new plant. The fixed costs are $100,000 per year. The marginal cost of production is $2 for a quantity up to 10,000 units per year. The marginal cost of production is $4 for a quantity between 10,001 and 30,000 units per year (an additional 20,000 units per year) and $I 0 for production above 30,000 per year.
1) 'What is the break even quantity or quantities if the market is competitive and the market price is $8 per unit?
2) If the market is competitive and the market price is $8 per unit, what production range would the plant operate?
3) What is the break even quantity if the fixed cost per year was $310,000 per year, the market is competitive and the market price is 412 per unit?
Q2. According to a study of U.S. cigarette sales between 1955 and 1985, when the price of cigarettes was 1% higher, consumption would be 0.4% lower in the short run and 0.75% lower in the long run (Becker et al., 1994)
a. Calculate the short-and long-run price elasticities of the demand for cigarettes.
b. Is demand more or less elastic in the long run than in the short run? Explain your answer.
c. If the government were to impose a tax that raised the price of cigarettes by 5 percent, would total consumer expenditure on cigarettes rise or fall in the short run? What about in the long run?
Q3. Suppose the chairman and chief executive officer of General Motors has decided to a) raise the company's auto prices by 5%. In addition, suppose that the following events have been forecast for the next year b) the price of competitors cars are due to rise by 8%; c) consumers' incomes will rise by 2%; and d) the price of gasoline is due to fall by 20%. You, as head of production, must decide what all of these events mean for GM's car sales so that you can plan production accordingly. You hire an economics consulting rum that provides you with these estimates based on econometric studies:
Price elasticity of demand for GM cars is 2.0 (in absolute value terms)
Cross price elasticity between GM cars and those of its competitors is +.5
Cross price elasticity between GM cars and gasoline is -.3
Income elasticity of demand for GM cars is +1.6
Calculate the effect of each of these four changes on demand based on the estimates provided. What is the net effect of all the changes taken together?
a. Increase the company's auto prices by 5%.
k, the price of competitors cars are due to rise by 8%; g. consumers' incomes will rise by 2%; and
4, the price of gasoline is due to fall by 20%. e. Net effect to demand
Q 4. Your company manufactures controllers used in the production of commercial air conditioning units. Your current price is $50 per controller. At that price the total quantity demanded is 4,000 spread over a large number of small customers. Fixed costs are $10,000 per month and marginal costs are $30 for production up to 10,000 units per month. Production cannot be pushed beyond 10,000 units per month. A hurricane has damaged the production facility of a company that produces a low-quality substitute controller. As a result that company has offered you a one-time $35,000 contract for 1,000 controllers to be delivered this month so they can meet the demand of their customers. Within a month the damage to that company's facility will be repaired and they will be back to normal production. Hence this event will not cause your demand curve to shift.
a) Before deciding on the contract you want to analyze your current market. What is the optimal rice of your controller if the price elasticity of demand is estimated to be -2 for prices between $45 and $65 per controller?
b) Would you recommend setting your price to that determined in part (a)? Explain why or why not
c) Would you recommend accepting the offered contract? Explain why or why not.
d) Does your answer to (c) change if your fixed costs are $12,000 per month? Explain why or why not.
Q 5. You have 10 individuals with values ($1, $2, $3, $4, $5, $6, $7, $8, $9, $10), and suppose you find a way to charge one price to the consumers whose values are ($1, $2, $3, $4, $5), and a different price to those consumers whose values are ($6, $7, $8, $9, $10). MC of production is $2.50.
a. What price should you charge to the second group?
b. What are your expected profits from selling to the second group?
c. What price should you charge to the first group?
d. If it costs $5 to implement this price-discrimination scheme (to identify the two groups and prevent arbitrage between them), should you do it?
Q 6. A corn farmer is considering two alternatives for selling his crop. The first is a contract where he can sell the rights to the future crop at planting. The second is to sell the crop after harvest Al harvest the fanner estimates that the price of corn will be $I 0 per bushel with probability .5 and $12 per bushel with probability .5. The farmer is averse to risk, and is willing to pay $50,000 to avoid the risk of damage to the crop while it is growing (e.g., from a tornado or flood). If the fanner uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 55,000 bushels. The cost of pesticides is $20,000. The other costs associated with planting and harvesting the crop total $450,000.
a. If the farmer decides to sell the crop at harvest will he be better off using pesticides or not using them? What is the farmer's expected profit in each case?
b. What is the maximum a purchaser would be willing to pay to the farmer for the rights to the future corn crop assuming they cannot monitor the farmer after purchasing the contract? Defend your answer.
c. Which alternative: (1) sale of rights prior to planting or (2) selling the crop after harvest yields the maximum expected benefit for the farmer considering his level of risk aversion?
Q7. Two companies, A and B, are considering entry into the same two markets: Asia or Australia. Due to financial constraints each company can only enter one of the two markets. The expected payoffs to each company for each possible entry scenario are as follows:
Company A Decision Company B Decision Payoff to A Payoff to B
Enter Asia Enter Asia $35M $50M
Enter Asia Enter Australia $50M 590M
Enter Australia Enter Asia $85M $60M
Enter Australia Enter Australia $40M $45M
a) Construct a game that represents the entry decision.
b) What type of game is it?
c) Identify all Nash equilibriums for the game.
d) Company A has hired you as a consultant What advice would you give them regarding this entry decision?
Q 8. Your company has developed a drug called Matrox that is an effective treatment for migraine headaches. You have just discovered that it can also be used for organ transplant patients to reduce the risk of organ rejection. The demand for migraine medications is considerably more elastic than the demand for drugs to reduce the risk of organ rejections. A study has indicated that the elasticity of demand for Matrox as a migraine medication is -4.0 but as a transplant drug it is -1.5. The current price of Matrox is $10 per dose; the marginal cost is $5 per dose. Should you use a price discrimination scheme for this product in these two markets? If so, how should you price Matrox in each market? If not, why not? Show all calculations.