Assignment
1. Assume Kodak's production function for digital cameras is given by Q = 100 (L0.7K0.3), where L and K are the number of workers and machines employed in a month, respectively, and Q is the monthly output. Moreover, assume the monthly wage per worker is $3,000 and the monthly rental rate per machine is $2,000. NOTE: Given the production function, the marginal product functions are MPL = 70 (L-0.3K0.3) and MPK = 30 (L0.7K-0.7).
a. If Kodak needs to supply 60,000 units of cameras per month, how many workers and machines should it optimally employ?
b. What are the total cost and average cost of producing the quantity given in (a)?
2. Recently, the Brazilian Association of Citrus Exports (Abecitrus) announced that orange production would be down 25 percent this year because of poor weather conditions, disease, and tree stress resulting from three straight bumper crops. What effect will the decreased production of oranges have on the demand for tomato juice?
3. You are an economic advisor to the Treasurer of the United States. Congress is considering increasing the sales tax on gasoline by $.03 per gallon. Last year motorists purchased 10 million gallons of gas per month. The demand curve is such that every $.01 increase in price decreases sales by 100,000 gallons per month. You also know that for every $.01 increase in price, producers are willing to provide 50,000 more gallons of gasoline to the market. The legislature has stated that the $.03 tax will increase government revenues by $300,000 per month and raise the price of gasoline by $.03 per gallon. Is this correct?
4. The demand for company X's product is given by Qx = 12 - 3Px + 4Py. Suppose good X sells for $3.00 per unit and good Y sells for $1.50 per unit.
a. Calculate the cross-price elasticity of demand between goods X and Y at the given prices.
b. Are goods X and Y substitutes or complements?
c. What is the own price elasticity of demand at these prices?
d. How would your answers to parts a and c change if the price of X dropped to $2.50 per unit?
5. A consumer spends all of her income on only one good. What is the income elasticity of demand for this good? What is the own price elasticity of demand for this good?
6. Suppose that Bob's indifference curves are perfectly L-shaped with the right angle occurring when Bob has equal amounts of both goods. What does this imply about Bob's willingness to trade one good for the other? Give examples of goods where this type of behavior might be expected?
7. Suppose you are the manager of a firm that produces Ultrasweet, a sugar substitute. Show graphically the effect of a reduction in the price of Sweet and Healthy, a competitor's product, on a typical consumer's consumption of Ultrasweet.
8. In order to encourage energy conservation, many public utility companies charge consumers a higher rate on units of electricity consumed in excess of some threshold amount. In contrast, a common marketing ploy by other firms is to offer "quantity discounts" to consumers who purchase large quantities of a good. To illustrate how these pricing schemes alter the typical consumer's opportunity set, suppose income = $100, Px = $2 if the consumer buys less than 40 units of X, Px = $3 if the consumer buys more than 40 units of X, and Py = $5. Draw the budget constraint. How would the budget constraint change if the price decreased to $1 after 40 units of X were consumed?
9. Use indifference curve and constraint analysis to analyze the behavior of employees who are paid:
a. An hourly wage rate of $4 per hour.
b. A fixed hourly wage of $4 per hour, plus an overtime bonus of $4 for every hour worked in excess of eight hours.
c. A fixed salary of $40 per day, plus $4 for each hour worked.
d. Which of the above schemes would yield the largest number of hours worked? Explain.