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HW9

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Econ 300
Assignment 9

  1. Dr. E. is an environmentalist and a critic of economics. On the Charlie Rose Show he attacks our textbook: ''That text is typical - it includes all of this nonsense about long-run supply elasticities for natural resources like oil or coal. Any idiot knows that, because the earth has a finite size, all supply curves for natural resources are perfectly inelastic with respect to price. How can a rise in price for, say, oil, lead to more oil when all our oil was created eons ago? Focusing on these ridiculously high elasticity numbers just detracts from studying our real need- the need to conserve.'' How would you defend the analysis in this book against this tirade?

  2. Suppose the daily demand curve for flounder at Cape May is given by

    $\displaystyle Q_{D}=1,600-600P$    

    where $ Q_{D}$ is demand in pounds per day and $ P$ is price per pound.

    1. If fishing boats land 1000 pounds one day, what will the price be?

    2. If the catch were to fall to 400 pounds, what would the price be?

    3. Suppose the demand for flounder shifts outward to

      $\displaystyle Q_{D}=2,200-600P.$    

      How would your answers to $ b$ and $ c$ change?

    4. Graph your results.

  3. Suppose as in the previous problem, the demand for flounder is given by

    $\displaystyle Q_{D}=1,600-600P$    

    but now assume that Cape May fisherman can, at some cost, choose to sell their catch elsewhere. Specifically asssume that the amount they will sell to Cape May is given by

    $\displaystyle Q_{S}=-1000+2000P$ for $\displaystyle Q_{s}\geq 0,$    

    where $ Q_{s}$ is the quantity supplied in pounds and $ P$ is the price per pound.

    1. What is the lowest price at which flounder will be supplied to the Cape May market?

    2. Given the demand curve for flounder, what will the equilibrium be?

    3. Suppose now, as in the previous problem, demand shifts to

      $\displaystyle Q_{D}=2,200-600P.$    

      What will be the new equilibrium price?

    4. Expalin intuitively why price will rise by less in $ c$ than it did in the previous problem.

    5. Graph your results.

  4. Suppose ther are $ 100$ identical firms in the perfectly competive notecard industry. Each firm has a short-run total cost curve of the form:

    $\displaystyle STC=q^{\frac{3}{300}}+0.2q^{2}+4q+10$    

    and marginal cost is given by

    $\displaystyle SMC=0.01q^{2}+0.4q+4.$    

    1. Calculate the firm's short-run supply curve with $ q$ (the number of crates of notecards) as a function of market price $ P.$

    2. Calculate the industry supply curve for the $ 100$ firms in this industry.

    3. Supplise market demand is given by

      $\displaystyle Q=-200P+8000.$    

      What will be the short-run equilibrium price-quantity combination?

    4. Suppose everyone starts writing more research papers and the new market demand is given by

      $\displaystyle Q=-200P+10,000.$    

      What is the new short-run price-quantity equilibrium? How much profit does each firm make?

  5. What is produced under perfectly comepetive conditions? Individual wheat farmers have $ U-$ shaped long-run, average-cost curves that reach a minimum average cost of $3 per bushel when $ 1000$ bushels are produced.

    1. If the market demand curve for wheat is given by

      $\displaystyle Q_{D}=2,600,000-200,000P$    

      where $ Q_{D}$ is the number of bushels demanded per year and $ P$ is the price per bushel, in long-run equilibrium what will be th eprice of wheat? How much total wheat will be demanded? How many wheat farms will there be?

    2. Suppose demand shifts outward to

      $\displaystyle Q_{D}=3,200,000-200,000P.$    

      If farmers cannot adjust their output in the short run (that is, suppose the SMC curve is vertical), what will market price be with this new demand curve? What will the profits of the typical farm be?

    3. Given the new demand curve described in $ b$ , what will be the new long-run equilibrium? That is, calculate market price, quantity of wheat produced, and the new equilibrium number of farms in this new situation.

    4. Graph your results.

  6. A perfectly competitive painted necktie industry has a large number of entrants. Each firm has an identical cost structure such that long-run average cost is minimized at an output of 20 units ($ q_{i}=20$ ). The minimum average cost is $10 per unit. Total market demand is given by

    $\displaystyle Q=1500-50P$    

    1. What is the industry's long-run supply schedule?

    2. What is the long-run equilibrium price ( $ P^{\ast })$ ? The total industry output $ \left( Q^{\ast }\right) ?$ The output of each firm $ \left( q_{i}^{\ast }\right) ?$ The number of firms? The profits of each firm?

    3. The short-run total cost curve associated with each firm's long0run equilibrium output is given by

      $\displaystyle STC=.5q^{2}-10q+200$    

      where

      $\displaystyle SMC=q-10.$    

      Calculate the short-run average and marginal cost curves. At what necktie output level does short-run average cost reach a minimum?

    4. Calculate the short-run supply curve for each firm and the industry short-run supply curve.

    5. Suppose now painted neckties become more fashionable and the market demand function shifts upward to

      $\displaystyle Q=2000-50P.$    

      Using this new demand curve, answer $ b$ for the very short run when firms cannon change their outputs.

    6. In the short run, use the industry short-run supply curve to recalculate the answers to $ b.$

    7. What is the new long-run equilibrium for the industry?

  7. The handmade snuffbox industry is compese of 100 identical firms, each having short-run total costs given by

    $\displaystyle STC=0.5q^{2}+10q+5$    

    and short-run marginal costs given by

    $\displaystyle SMC=q+10$    

    where $ q$ is the output of snuffboxes per day.

    1. What is the short-run supply curve for each snuff-box market? What is the short-run supply curve for the market as a whole?

    2. Suppose the demand for total snuffbox production is given by

      $\displaystyle Q=1,100-50P.$    

      What is the equilibrium in this marketplace? What is each firm's total short-run profit?

    3. Graph the market equilibrium and compute total producer surplus in this case.

    4. Show that the total producer surplus you calculated in part $ c$ is equal to total industry profits plus industry short-run fixed costs.

  8. Consider the market for broccoli where

    $\displaystyle Q_{d}=1000-5P$    

    and

    $\displaystyle Q_{s}=4P-80.$    

    1. What is the equilbrium price and quantity?

    2. Suppose demand increases to

      $\displaystyle Q_{d}=1270-5P.$    

      What is the equilbrium price and quantity?

    3. What are the levels of consumer and producer surplus?

    4. Suppose the government has prevented the price of broccoli from rising from its equilibrium price in $ a.$ Describe how the CS and PS measures described in $ c$ would be reallocated or lost entirely.

    5. Return to the original demand curve in $ a$ . Suppose the government instituted a $45-per-hundred bushel tax on broccoli. How would this tax affect equilibrium in the broccoli market? How would this tax burden be shared between buyers and sellers of broccoli? What is the excess burden of this tax?


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Jenn Thacher 2008-08-25
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