Questions 1-3.
To answer these questions you need to draw the demand and supply curves.
Read pages 23-29 of your text for very detailed instructions about how
to draw demand and supply curves.
You will find the competitive equilibrium price and quantity at the crossing of these two curves.
A discussion of how to calculate firms' profits in competitive is found on pages 33-35. The idea is simple. You have found that the competitive equilibrium price is $30. At a price of $30, the growers with $30 costs make no profits, whether or not they sell any bananas. The 10 growers with $15 costs each make a profit of $15, so the total profit of growers is $150.
Questions 4-6
To answer these questions, you again need to draw the demand curve and
the supply curve.
The demand curve has "steps" at prices of $30, $20, $10, and $0.
The steps at $30, $20, and $10, are each 100 units long. Each day
the supply curve is vertical. (See Chapter 2) On Monday the total
number of fish caught is 60 and the vertical supply curve drawn at x=60
intersects the demand curve where price=$30. On Tuesday, 80 fish
are caught and the vertical supply at x=80 intersects demand at a price
of $30. On Wednesday the number of fish caught is 160 and the vertical
supply at x=160 intersects the demand curve at price=$20. On Thursday,
the number of fish caught is 240 and supply intersects demand at a price
of $10, on Friday, the number of fish caught is 320 and supply intersects
demand where price is $0. To calculate profits, multiply price times
quantity and subtract $100. . On Monday, each fisherman makes (3x$30)-$100=$-10,
on Tuesday, each fisherman makes (4x$30)-$100=$20, on Wednesday, each fisherman
makes (8x$20)-$100=$60, on Thursday, each fisherman makes (12x$10)-$100=$20
and on Friday, each fisherman makes (16x$0)-$100=$-100.
If the price of fuel rises from $100 to $150, fishermen will still want to supply everything they catch So the supply curve each day will still be a vertical line at the number of fish caught.. Since neither the supply curve nor the demand curve is any different than it was when fuel cost $100, the price will not change. Of course profits of fishermen will be $50 lower, no matter what they do. (See pages 67 and 68 of the text.)
7. The demand curve crosses the supply curve when 100-Q=10+Q/2. Solving this equation we see that this happens when Q=60. The question asks for the competitive equilibrium PRICE. To find this price, remember that P=100-Q and that Q=60, so P=40. (See pp 87-88 of the text.)
8. An increase in the number of rainy days will make more people want umbrellas at any given price. This shifts the demand curve outwards. The rainy days will have no particular effect on the costs of producing umbrellas, so the supply curve will not change. The new equilibrium will be where the new demand curve meets the same old supply curve. If the supply curve is upward sloping, this will have to be at a point where the price is higher and the quantity is higher. (See pages 69-75 of the text for a detailed discussion of the effects of shifting demand curves.)
9. The frost will shift the supply curve leftwards, since at any price the number of oranges that farmers will supply is now lower. The frost will have no effect on the number of oranges that consumers will demand at a given price. The new supply curve will cross the old demand curve at a higher price and lower quantity than before the frost. (See pages 69-75 of the text for a detailed discussion of the effects of shifting demand curves.)
10. An increase in both price and quantity is consistent with an outward (upward) shift in the demand curve where there is an upward-sloping supply curve. The diagram on page 75 of your text shows how this works.
11. There is no reason to expect that demanders and suppliers make equal profits in competitive equilibrium. You have done several experiments in which this is not the case.
12. Just draw the curves to see that this happens.
13. See page 33 of the text for the definition of consumers' surplus.
14. We intended the answer to this to be "true". And it is true when the supply curve crosses the demand curve at a single point. But an alert student pointed out to us that in case the supply curve and demand curve meet on an interval as is illustrated on page 107 of the text, there can be more than one competitive equilibrium price and so it is possible that in competitive equilibrium some people are paying different prices from others. Because of this, we are giving full credit for either an answer of "true" or an answer of "false".
15. Competitive equilibrium does not maximize the number of profitable
trades. It does maximize the total amount of profits. See the discussion
on pages 47-48.