Microeconomics Short Solutions - Assignment Example

Microeconomics Short Solutions A is providing free flu shots to and faculty at 4 different locations and s around campus this fall. What would you expect to see at these events? Describe the situation with a Marshallian cross diagram. Let’s say that 2 of these events are held at convenient locations and times and the other two are not. Illustrate this on a Marshallian cross diagram. If the university charged a fee for the shots, what would change? If the flu shots are free, it is expected that people will come willingly to the event, and thus quantity demanded is as much as quantity supplied. In the graph, this is shown as Qs1 = Qd1, which is the red line that coincides with the x-axis, at which line price is nil (P = 0). Supposing, however, that two of the events are located at convenient locations and times and two are not, it is possible that this would discourage students and faculty who are close to these areas, reducing the quantity demanded from that supplied during these event. This would bring quantity to Qd1’, in comparison to Qs1 which remains constant. (This is of course supposing that quantity supplied, or number of vaccine shots prepared, is fixed per event. It would be possible, in this case, for more of the students and faculty to flood the two conveniently scheduled events, making quantity demanded exceed quantity supplied during those events.) If the university charged a fee for the shots, the demand curve would change to D2 and the supply curve to S2 if the four events were all conveniently scheduled. If two of the events were inconveniently scheduled, the demand curve would move lower to D2’. Consequently, we will find the equilibrium quantity and price at Qe2 and Pe2 for all four events being convenient, and likewise Qe2’ and Pe2’ for the events being scheduled at inconvenient places. The graph below assumes that the fee for the vaccine is variable; however, if the fee is fixed, S2 will be a horizontal line, Pe2 and Pe2’ will be constant for both convenient and inconvenient schedules, and only Qe2 and Qe2’ will be different. 2a. Automobile insurance companies charge premiums based on past driving history (including collisions, traffic violations, etc). How does this influence the behavior of motorists? Since premiums were based on past diving history, the occurrence of accidents and violations would cause premiums to rise for motorists. Therefore, motorists would tend to be more careful in driving in order not to incur any adverse incidents, so as to avail of low premiums. 2b. Health insurance companies do not charge premiums based on past health history. How does this influence behavior of the population? The fact that premiums for health insurance are not based on past health history does not materially affect the choice of people to be more or less cautious about their health. Human behavior is such that persons are prone to maintain habits, whether for their good or bad, as a matter of psychological motivation. For instance, a person will not quit smoking for the sole reason of avoiding higher premiums; he will continue to smoke if it gives him pleasure. If anything, the danger of cancer or of poor health in advanced age should be a greater deterrent to adopting or continuing with poor health habits. As for illness or accidents, since they are unintentional and occur spontaneously, their occurrence is not dependent upon the size of health insurance premiums. 3. The table below shows the marginal valuation which Sally and Tom place on various numbers of Grate Full Dead rock concert tickets. Number Of Tickets 1 2 3 4 5 6 7 8 9 Marg Value By Sally 60 40 30 25 22 20 18 12 8 Marg Value By Tom 25 20 18 15 12 10 8 5 3 3a. Assume that someone has given 5 tickets to Sally and 5 tickets to Tom. If Tom and Sally can exchange (buy and sell) tickets, who would buy tickets from whom? At 5 tickets each, Sally would tend to buy tickets from Tom, because she still has a higher marginal valuation at 5 tickets. Sally will buy Tom’s 5th and 4th tickets, because: Sally’s sixth ticket MV: 20 > 12 : Tom’s 5th ticket MV Sally’s seventh ticket MV: 18 > 15 : Tom’s 4th ticket MV But Sally’s eight ticket MV: 12 < 18 : Tom’s 3rd ticket MV Thus, Sally will be expected to buy 2 tickets from Tom. 3b. Alternatively, assume that Tom is given 10 tickets and Sally gets none. If they can exchange, what final disposition of tickets do you expect. In that case, Sally will purchase seven tickets from Tom. She will continue to purchase until her MV of the next ticket she will buy will equal or be less than Tom’s MV of the next ticket he will sell. Sally’s 1st ticket MV 60 > 0 : Tom’s 10th ticket MV 2nd ticket MV 40 > 3 : 9th ticket MV 3rd ticket MV 30 > 5 : 8th ticket MV 4th ticket MV 25 > 8 : 7th ticket MV 5th ticket MV 22 > 10 : 6th ticket MV 6th ticket MV 20 > 12 : 5th ticket MV 7th ticket MV 18 > 15 : 4th ticket MV But 8th ticket MV 12 < 18 : 3rd ticket MV Thus, Sally will be expected to buy up to 7 tickets from Tom. 4. Assume that a specific tax of $2 is placed on cigarettes and that the price of cigarettes rises by exactly $2. What does this suggest about the demand for and supply of cigarettes? Since the $2 specific tax did not affect the equilibrium quantity demanded or supplied of cigarettes, shown by the equilibrium price merely reflecting the tax and no asymmetry introduced, then it may be said that the demand and supply of cigarettes are not dependent upon price components such as tax. The price elasticity of demand for cigarettes is considered relatively inelastic, and given small changes in price cigarette smokers will still buy the same quantity of cigarettes as they did previously. 5a. Nazmul’s marginal utility of apples is given by MUApples = 30 – 2A, where A is apples per week. His marginal utility of bananas is given by MUBanana = 100 – 5B, where B is bananas per week. If the price of apples equals the price of bananas, and you observe Nazmul eating 18 bananas per week, how many apples should he be eating? At optimum point, the marginal utility should equal the marginal cost. In this case, price being constant per additional piece, the price is the marginal cost. Price should thus be equal to marginal utility at optimum point, and from the given MUBanana = MUApples. If B = 18, then MUBanana = 100 – 5B = 100 – 5 (18) = 10 MUApples = 10 = 30 – 2A Therefore, A = (30 – 10) / 2 = 10 apples Nazmul will thus be able to eat 10 apples a week. 5b. Now assume that the price of bananas is twice the price of apples and you now see Nazmul eating 17 bananas per week. How many apples should Nazmul be eating? From the given, MUBanana = 2 x MUApples. Thus, 100 – 5B = 2 x (30 – 2A) 100 – 5 x (17) = 2 x (30 – 2A) Therefore, A = 15 apples 6a. Yi Songs demand for hotdogs is given by H = 30 ‑ 0.5PH, where H = hotdogs per month and PH is the price of hotdogs in cents. If the price of hotdogs, PH = 50, what is her price elasticity of demand for hotdogs? (hint: what happens to H if PH changes a bit?) When price falls, does her total expenditure on hotdogs rise? At PH = 50, Yi Song’s demand for hotdogs will be H = 30 - 0.5 (50) = 5 At PH = 48, her demand for hotdogs will be H = 30 - 0.5 (48) = 6 Her price elasticity for hotdogs at this price is thus ∆H / H 1 / 5 Ep = --------------- = ------------ = -5 ∆ PH / PH -2 / 50 Her total expenditure changes by: 6 (48) - 5 (50) = 288 - 250 = 38 (upwards) Thus, at PH = 50, when price falls slightly, Yi Song’s total expenditure rises. 6b. What is the own price elasticity of Yi Songs demand for hotdogs if PH = 10 cents? When price falls, does total expenditure rise? At PH = 10, Yi Song’s demand for hotdogs will be H = 30 - 0.5 (10) = 25 At PH = 8, her demand for hotdogs will be H = 30 - 0.5 (8) = 26 Her price elasticity for hotdogs at this price is thus ∆H / H 1 / 25 Ep = --------------- = ------------ = -0.2 ∆ PH / PH -2 / 10 Her total expenditure changes by: 26 (8) - 25 (10) = 208 - 250 = -42 (downwards) Thus, at PH = 10, when price falls slightly, Yi Song’s total expenditure falls. 7. Ge Baos marginal utility of sweaters and blouses is shown below: Number of Units 1 2 3 4 5 6 7 8 9 Marg. Utility Sweat 200 180 160 120 100 80 60 40 25 Marg. Utility Blouse 500 400 300 250 200 100 50 10 0 Assume that sweaters cost $50/each and that blouses costs $200 each. Compute the marginal utility per dollar spent on sweaters and on blouses. If you are told that Ge Bao buys 5 sweaters, how many blouses will she buy? If Ge Bao buys 2 blouses, how many sweaters will she buy? Ge Bao’s marginal utility per dollar is arrived at by dividing the marginal utility for that quantity by the price respective price ($50 for sweaters and $200 for blouses). Thus, Ge Bao’s marginal utility for sweaters and blouses is as follows: Number of Units 1 2 3 4 5 6 7 8 9 MU/$ Sweat 4 3.6 3.2 2.4 2 1.6 1.2 0.8 0.5 MU/$ Blouse 2.5 2 1.5 1.25 1 0.5 0.25 0.05 0 If Ge Bao buys 5 sweaters, that indicates she is willing to spend to acquire a marginal utility of 2 for every dollar. With this as basis, it is assumed that she also would spend as much for blouses, and thus would buy 2 blouses, which gives her the same MU/$. Likewise, if she buys 2 blouses, she will be expected to buy 5 sweaters, which has the same MU/$. 8. Tonys Spa in Alderson, WVA provides massage treatments available under 3 different pricing schemes: regular package $30 per treatment; members package $20 per treatment and a members fee of $180 per month; and inmates package with unlimited treatments and a $700 per month fee. It Marthas demand for massage treatments is given by M = 30 - 0.5P, where M is treatments per month and P is price per treatment, which option will Martha choose and how many monthly treatments will she have? First Option: At the regular package priced $30 per treatment, Martha’s demand will be M = 30 – 0.5 (30) = 15 treatments At this price, Martha intends to spend 15 (30) = $450. Second Option: For the member’s package of $20 per treatment and a member’s fee of $180 per month, the member’s fee qualifies the price. The more the demand, the smaller the effect of the member’s fee per treatment. Thus the price per treatment of the second scheme is: 180 P = 20 + ---------- M and Martha’s demand for treatments would be described by the equation: 180 M = 30 – 0.5 (20 + ---------) M Distributing the terms and multiplying both sides of the equation by M yields a quadratic equation: M2 = 30M - 10M - 90 = 20M - 90 M2 – 20M + 90 = 0 Using the quadratic equation, ax2 + bx + c = 0, Thus, for the member’s scheme, M1 = 10 + 3.1622 = 13.1622 treatments, or M2 = 10 - 3.1622 = 6.84, or approximately 7 treatments. For M1 = 13 treatments, this would cost Martha $20 (13) + 180 or $ 440, while M2 = 7 treatments would cost Martha $20 (7) + 180 = $ 320. It is apparent that neither of these solutions are better than the first scheme, because they have average costs of $33.85 and $45.71 per treatment, both more expensive than the first option. Third Scheme: The price would be $700 distributed over M treatments. Therefore, 700 M = 30 - 0.5 (--------- ) or M2 – 30M + 350 = 0 M Using the quadratic formula, M is found to be indefinable because the quadratic formula calls for the square root of a negative number. Therefore, the optimum solution is still the first option, the regular rate at $30 per treatment. She should have 15 monthly treatments. 9) For years cows have been artificially inseminated. The result was production of equal numbers of male and female calves and hence equal numbers of cows and bulls. The price of cows was above the price of bulls (partly due to price supports for milk). Show this market equilibrium on two supply and demand curves. Recently advances in cow fertility allow breeders to select the sex of the offspring (they can choose to produce a cow or steer). What should happen to the ratio of cows to steers born if sex can be selected? What will happen to the price of cows and steers? Show this on your Marshallian cross diagrams. What will happen to the supply of milk? When there is an equal production of cows and bulls, since the cows are considered more valuable than the bulls then it will naturally command a higher price. In the first graph the demand for cows is shown by the purple line denoted by Dc which is to the right of the blue demand curve for bulls, Db. This depicts the higher demand for cows. On the other hand, the red supply curve for cows, Sc, has a steeper inclination than that for bulls (the orange supply line Sb), since breeders would prefer to sell cows only at the higher price. As already mentioned, the equilibrium quantity for both bulls and cows should be the same, Qc = Qb, because the quantities bred per gender are the same. The equilibrium price of cows Pc will be situated higher than that for bulls, Pb. Upon the condition that the ratio of bulls to cows may be selected, then the graph will adjust to that shown in the figure below. Breeders will tend to produce more cows than bulls (Qc > Qb) because of the higher price they commanded. However, because there are now more cows than bulls, their price will adjust downward and the price of bulls upward, so that at some point they will come close or even equal each other. (Pc=Pb). At this point, the supply curve for cows (Sc) would have adjusted to a more gradual slope, maybe even lower than the supply curve for bulls. The demand curves for cows and bulls, Dc and Db, are not foreseen to be materially affected by the ratio of cows to bulls, as cows are still seen to be more valuable because of the support for milk prices. However, with the greater production of cows, it is expected that the supply for milk will also increase, thereby easing the pressure on the price of milk. Read More