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HW6

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Econ 300
Assignment 6

  1. ''Gaining extra revenue is easy for any producer-all that it has to do is raise the price of its producer.'' Do you agree? Explain when this would be true, and when it would not be true.

  2. Table 4.4 (in the book) reports an estimated price elasticity of demand of $ -1.14$ for electricity$ .$ Explain what this means with a numerical example. Does this number seem large? Do you think this is a short or long-term elasticity estimate? How might this estimate be important for owners of electric utilitites or for bodies that regulate them?

  3. Table 4.5 (in the book)reports that the cross-price elasticity of demand for electricity with respect to the price of natural gas is $ 0.50$ . Explain what this means with a numerical example. What does the fact that the number is positive imply about the relationship between electricity and natural gas use?

  4. The market demand for cashmere socks is given by

    $\displaystyle Q=1000+0.51-400P+200P^{\prime }$    

    where
    $\displaystyle Q$ $\displaystyle =$ Annual demand in numbers of pairs  
    $\displaystyle I$ $\displaystyle =$ Average income in dollars per year  
    $\displaystyle P$ $\displaystyle =$ price of one pair of cashmere socks  
    $\displaystyle P^{\prime }$ $\displaystyle =$ Price of one pair of wool socks.  

    Given that $ I=\$20,000$ , $ P=\$10$ , and $ P^{\prime }=\$5$ , determine $ % \varepsilon ^{Q,P},\varepsilon ^{Q,I},\varepsilon ^{Q,P^{\prime }}.$

  5. Fill in the table below.

    $ D(p)$ Price Elasticity of Demand
    $ D(p)=60-p$  
    $ D(p)=a-bp$  
    $ D(p)=40p^{2}$  
    $ D(p)=Ap^{-b}$  
    $ D(p)=(p+3)^{-2}$  
    $ D(p)=(p+a)^{-b}$  

  6. An economic historian (Gavin Wright, The Political Economy of the Cotton South, 1978) reports that econometric studies indicate that for the pre-Civil war period, 1820-1860, the price elasticity of demand for cotton from the American South was approximately $ -1.$ Due to the rapid expansion of the British textile industry, the demand curve for American cotton is estimated to have shifted outward by about $ 5\%$ per year during this entire period.

    1. If during this period, cotton production in the US grew by about $ 3\%$ per year, what (approximately) must be the rate of change of the price of cotton during this period?

    2. Assuming a constant elasticity of $ -1$ , and assuming that when the price is $ \$20$ the quantity is also $ 20$ , graph the demand curve for cotton. What is the total revenue when the price is $ \$20$ ? What is the total revenue when the price is $ \$10$ ?

    3. If the change in the quantity of cotton supplied by the US is to be interpreted as a movement along an upward-sloping long-run supply curve, what would the elasticity of supply have to be? (Hint: form 1820 to 1860, quantity rose about 3% per year and price rose by ____ % (see previous answer). If the quantity change is a movement along the long-run supply curve, then the long-run price elasticity must be what?)

    4. The American Civil War, beginning in 1861, had a devastating effect on cotton production in the South. Production fell by about $ 50\%$ and remained at that level throughout the war. What would you predict would be the effect on the price of cotton?

    5. What would be the effect on total revenue of cotton farmers in the South?

    6. The expansion of the British textile industry ended in the 1860s and for the remainder of the nineteenth century, the demand curve for American cotton remained approximately unchanged. By about 1900, the South approximately regained its prewar output level. What do you think happened to cotton prices then?

  7. In a famous anti-trust case, the US Department of Justice brought suit against the Du Pont chemical company for having monopolized the sale of cellophane. In its defense, Du Pont utilized measurements of the cross-price elasticities between cellophane and the following products: aluminum foil, waxed paper, and polyethlene. The Supreme Court accepted Du Pont's argument in a landmark decision handed down in 1953. In a few sentences, summarize Du Pont's argument and how it made uses of these measurements.

  8. Suppose we know that originally the demand for drugs in the US is $ % Q^{d}=100-.1P$ and the supply of drugs is $ Q^{s}=50+.5P$ . The government has two possible policy options if its goal is to decrease the quantity of drugs in the market: a program to decrease supply by putting drug dealers in jails (''war on drugs'') OR a program to decrease demand by offering drug rehabilitation treatment. If the government institutes a rehabilitation program, demand decreases to $ Q^{d^{\prime }}=90-.09P$ . If the government institutes a ''war on drugs'', supply falls to $ Q^{s\prime }=45+.45P$ .

    1. Which program is more effective if the goal is to decrease the amount of drugs sold?

    2. Calculate $ \varepsilon ^{d}$ and $ \varepsilon ^{s}$ . Make a statement about the relative effectiveness of these 2 policies based on the elasticity of supply and demand. Explain the intuition.

  9. The coconut oil demand function (Beuschena and Perloff, 1991) is

    $\displaystyle Q=1,200-9.5P+16.2p_{p}+0.2Y$    

    where $ Q$ is the quantity of coconut oil in cents per pound, $ p_{p}$ is the price of palm oil in cents per pound, and $ Y$ is the income of consumers. Assume that $ p$ is initially $ 45$ cents per pound, $ p_{p}$ is $ 31$ cents per pound$ ,$ and $ Q$ is $ 1,275$ thousand metric tons per year.

    1. Calculate the price and cross-price elasticities of demand for coconut oil.

    2. Calculate the income elasticity of demand for coconut oil. (If you don't have all the numbers necessary to calculate numerical answers, write your answers in terms of variables)


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Jenn Thacher 2008-08-25
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