Assignment 1 Solutions October 6, 2017
All subquestions are worth 2 points, for a total of 76 marks. PLEASE READ THE SOLUTION TO QUESTION 3. Question 1 1. An indifference curve is all combinations of the two consumption goods that the individual is indifferent between. 2. Highly curved: Pencils and paper are complementary. 3. Less curved: Glasses and contacts are fairly substitutable. For some people, perhaps they are complimentary. Maybe they like glasses for the evenings, and contacts for the day. Specific example: 1. 50 = 10Q +5R 2. Slope of the budget constraint is -5/10 = -1/2. The Y-intercept is 50/10 = 5, and the X-intercept is 50/5 = 10. 3. The entire area below and on the budget constraint is affordable. Everything above the budget constraint is not affordable. 4. The slope of the indifference curve is equal the slope of the budget line, at the optimal consumer choice, which is -1/2. 5. The Y-intercept decreased to 50/15. The X-intercept remained the same. 6. The slope of the budget constraint is now -5/15 = - 1/3. This will be the slope of the indifference curve at the optimal choice. 7. The slope of the indifference curve represents how much quinoa the consumer is willing to trade for one unit of rice (in order to remain indifferent). 8. The new budget curve shifts outward. The slope is still -1/3. The new Y and X intercepts are 100/15 and 100/5 respectively. 1
Question 2 3. We plot demand curves with price on the vertical axis, and quantity on the horizontal. The vertical axis intercept (where Q=0) is 5, and the horizontal axis intercept (where P=0) is 20. 4. The slope ( P/ Q) is -1/4. 5. Recall our formula for the elasticity at a specific point is Q Q P = 4, then the price elasticity of demand is -4. P P Q. If price is 4, Q =4, and 6. If price is 2, quantity is 12. The slope is the same. Therefore, the elasticity is 2/3 7. I gave everyone full marks on this question, regardless of your answer. Think about an example. If ramen noodles increase from 5 cents to 10 cents ( a 100 percent increase in price), would your demand change much? Probably not. The price is still very low. However, if the price of ramen started at 2 dollars, then increased to 4 dollars (a 100 percent increase), that would substantially affect my demand. For linear demand curves, the elasticity will always increase (in absolute value terms) as the price rises. Of course, linear demand curves are not very realistic. Some highlycurved demand curves will not have the same relationship between price and elasticity. 8. Attention here: Most people in the class said the demand curve will shift rightwards simply because the person has more money. This is not always true. It depends if the good is normal or inferior. Wine is a normal good - demand increases with income. Other things like rice might be inferior - increases in income might cause demand to fall as people substitute towards tastier foods. I gave full marks, regardless of whether you drew this distinction. On the exam, I will not. 9. Beer is typically considered a substitute for wine. If beer becomes more expensive, people will demand more of wine. Demand curve shifts right. Question 3 1. An isoquant represents all combinations of the two inputs that produce the same amount of output. 2. It is hard to say. As long as you justified your answer, you got full marks. If you said perfect complements, you lost half a mark, because it is unrealistic to think that a computer for a firm is useless without a secretary to go with it. 2
3. The isoquant representing more output is further out. 4. Attention Here: I made a poor semantic choice. In tutorials, and in the tutorial notes, I defined the cost curve as the line that represents all combinations of inputs that together cost the same amount. In Kevin s slide s, he called this the firm s budget constraint. These were both poor choices. Most textbooks call this the iso-cost line. In firm-side economics, the cost curve sometimes refers to the relationship between total cost and total output. We have not covered this. Nonetheless, some of you used this definition. You only lost minimal marks for doing this, depending on whether the rest of your answer was consistent with this definition. 5. The slope of the cost curve (iso-cost) represents the ratio of the input prices. This is how much of one input can be replaced with the other, while holding total cost constant. If you defined the cost curve differently (as described above), then the slope would be the marginal cost of output. We have not covered this. 6. The slope of the isoquant represents the rate at which the two inputs can be substituted without changing output. Now the specific example: 1. The Y-intercept (robots) is 2000/100 = 20. The X-intercept (workers) is 2000/200 = 10. 2. The slope is -200/100 = -2. This is the ratio of the input prices. 3. For a given total cost, the Y-intercept represents the number of robots the firm would use if it didn t use any workers. Similarly for the X-intercept. 4. The slope of the isoquant at the optimal input choice will be the same as the slope of the cost curve (iso-cost) = -2. 5. The new cost curve (iso-cost) shifts inwards. The slope has not changed. The new Y and X-intercepts are 1000/10 and 1000/20 respectively. 3
Question 4 3. The supply curve starts at (Q= 500, P=0), then continues upwards. The slope is (1/100). 4. Quantity supplied is 1000. Price elasticity of supply is Q P = 100 5 = 1/2. P Q 1000 5. Higher wages mean higher production costs. This shifts the supply curve to the left. 6. If production costs decrease, the supply curve shifts right. Question 5 3. To find the equilibrium price and quantity, set quantity demanded equal to quantity supplied. 100 50P = 400 25P, and solve for P = 4. At a price of four, quantity is 300. To check your algebra, you can plug 4 into both the supply and demand equations. The result should be the same. 4. Using the same formula as always, the price elasticity of demand is -1/3, and the price elasticity of supply is 2/3. 5. The new price is 2, and quantity 200. 6. The new elasticity of demand is -1/4. You got full marks, regardless of if you explained why it changed. See the explanation in question 2. 4