to Answers ECON 201 Practice Problems Midterm II
1. Is it possible for marginal utility to be negative while total utility is positive? If so, explain how. If not, explain why not. Yes, it is possible. If marginal utility is negative, that means that total utility is decreasing. However, as long as the marginal utility of the next unit is less (in absolute value) than the total utility associated with the current level of consumption, then total utility will still be positive once the next unit is consumed. In that situation, the marginal utility of the last unit will be negative, but total utility will still be positive. Take a look at the example in our notes of the marginal utility I get from receiving a 6th guitar and my total utility from receiving 6 guitars to see whats going on. 2. Jim allocates his budget of $24 per week among three goods. Use the following table of the marginal utilities of good A, good B, and good C to answer the questions below. QA 1 2 3 4 5 MUA 50 40 30 20 15 QB 1 2 3 4 5 MUB 75 60 40 30 20 QC 1 2 3 4 5 MUC 25 20 15 10 7.5
a. If the price of A is $2, the price of B is $3, and the price of C is $1, how much of each good will Jim purchase in order to maximize his utility? Jim will purchase 4 units each of goods A, B and C. The per dollar marginal utility (the ratio of marginal utility to price) is equal to 10 for each good, and Jim spends all of his $24 ($8 on A, $12 on B and $4 on C). b. If the price of A rises to $4 while other prices and Jims budget remain unchanged, how much of each will he purchase in equilibrium? Jim will now purchase 2 units of A and 4 units of both B and C. The per dollar marginal utility is 10 for each good, and Jim spends all of his $24 ($8 on A, $12 on B and $4 on C). c. Using the information from parts (a) and (b), draw Jims demand curve for good A. Be sure to indicate the price and quantity demanded for each point on the curve. P
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3. What is the difference between fixed and variable cost? Do both types of costs affect short run marginal cost? If so, explain how each affects marginal cost. If not, explain why each does or does not affect marginal cost. A fixed cost is a cost for a firm in the short run that does not vary with output. Fixed costs are associated with resources which cannot be changed in the short run. Firms must pay fixed costs in the short run regardless of whether or not they produce any output. A variable cost is a cost for a firm that varies with output, and are associated with resources that can vary in the short run. If a firm chooses not to produce in the short run, it incurs no variable costs. Because marginal cost measures the change in total cost as output increases by one unit, it is only affected by the firms variable costs, since by definition fixed costs do not vary with output.
4. Explain why the marginal cost curve intersect must the average total cost curve and the average variable cost curve at their minimum points. Why do the average total cost and average variable cost curves approach one another as output increases? If average cost is falling, marginal cost must lie below average cost. If average cost is rising, marginal cost must lie above average cost. An average can only increase if the marginal amount is greater than the previous average. Average cost (AC) and average variable cost (AVC) differ only by average fixed cost (AFC), which is equal to fixed cost divided by quantity. As quantity increases, AFC must decrease (because the numerator of the fraction is fixed, but the denominator is getting larger), so AC and AVC must be getting closer and closer together. 5. The output level where average total cost is at a minimum is greater than the output level where average variable cost is at a minimum. Why is this the case? As output increases, the average fixed cost (AFC) must fall. Therefore, as output increases, average cost (AC) is pulled down by the AFC falling, since AC = AVC + AFC. Once the AVC curve begins to increase, AC will still fall to the extent that AFC is falling faster than AVC is rising. Eventually, AVC will rise faster than AFC falls, so that the AC curve will start to increase, but this will occur at a quantity greater than that associated with the minimum of the AVC curve. 6. Suppose that a certain manufacturer has a monopoly on the sorority and fraternity ring business (a constant cost industry) because it has persuaded the Greek community to give it exclusive rights to their insignias. a. Using demand and cost curves, draw a diagram depicting the firms profit maximizing price and o...