Al Deardwarf’s cousin, Zwerg, makes plaster garden gnomes. The technology in the garden gnome business is as follows. You need a gnome mold, plaster, and labor. A gnome mold is a piece of equipment that costs $1,000 and will last exactly one year. After a year, a gnome mold is completely worn out and has no scrap value. With a gnome mold, you can make 500 gnomes per year. For every gnome that you make, you also have to use a total of $7 worth of plaster and labor. The total amounts of plaster and labor used are variable in the short run. If you want to produce only 100 gnomes a year with a gnome mold, you spend only $700 a year on plaster and labor, and so on. The number of gnome molds in the industry cannot be changed in the short run. To get a newly built one, you have to special-order it from the gnome-mold factory. The gnome-mold factory only takes orders on January 1 of any given year, and it takes one whole year from the time a gnome mold is ordered until it is delivered on the next January 1. When a gnome mold is installed in your plant, it is stuck there. To move it would destroy it. Gnome molds are useless for anything other than making garden gnomes.
For many years, the demand function facing the garden-gnome industry has been D(p) = 60, 000−5, 000p, where D(p) is the total number of garden gnomes sold per year and p is the price. Prices of inputs have been constant for many years and the technology has not changed. Nobody expects any changes in the future, and the industry is in long-run equilibrium. The interest rate is 10%. When you buy a new gnome mold, you have to pay for it when it is delivered. For simplicity of calculations, we will assume that all of the gnomes that you build during the one-year life of the gnome mold are sold at Christmas and that the employees and plaster suppliers are paid only at Christmas for the work they have done during the past year. Also for simplicity of calculations, let us approximate the date of Christmas by December 31.
(a) If you invested $1,000 in the bank on January 1, how much money could you expect to get out of the bank one year later? _______. If you received delivery of a gnome mold on January 1 and paid for it at that time, by how much would your revenue have to exceed the costs of plaster and labor if it is to be worthwhile to buy the machine? (Remember that the machine will be worn out and worthless at the end of the year.) _______.
(b) Suppose that you have exactly one newly installed gnome mold in your plant; what is your short-run marginal cost of production if you produce up to 500 gnomes? _______. What is your average variable cost for producing up to 500 gnomes? _______. If you have only one gnome mold, is it possible in the short run to produce more than 500 gnomes? _______.
(c) If you have exactly one newly installed gnome mold, you would produce 500 gnomes if the price of gnomes is above _______ dollars. You would produce no gnomes if the price of gnomes is below _______ dollars. You would be indifferent between producing any number of gnomes between 0 and 500 if the price of gnomes is _______ dollars.
(d) If you could sell as many gnomes as you liked for $10 each and none at a higher price, what rate of return would you make on your $1,000 by investing in a gnome mold? _______. Is this higher than the return from putting your money in the bank? _______. What is the lowest price for gnomes such that the rate of return you get from ivesting $1000 in a gnome mold is as at least 10%? _______. Could the long-run equilibrium price of gnomes be lower than this? _______.
(e) At the price you found in the last section, how many gnomes would be demanded each year? _______. How many molds would be purchased each year? _______. Is this a long-run equilibrium price? _______.