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Imagine a society that produces military goods and consumer goods, which we'll call "guns" and "butter."a. Draw a production possibilities ...

Question

Imagine a society that produces military goods and consumer goods, which we'll call "guns" and "butter."a. Draw a production possibilities frontier for guns and butter. Explain why it most likely has a bowedout shape.b. Show a point that is impossible for the economy to achieve. Show a point that is feasible but inefficient.c. Imagine that the society has two political parties, called the Hawks (who want a strong military) and the Doves (who want a smaller military). Sho

Imagine a society that produces military goods and consumer goods, which we'll call "guns" and "butter." a. Draw a production possibilities frontier for guns and butter. Explain why it most likely has a bowedout shape. b. Show a point that is impossible for the economy to achieve. Show a point that is feasible but inefficient. c. Imagine that the society has two political parties, called the Hawks (who want a strong military) and the Doves (who want a smaller military). Show a point on your production possibilities frontier that the Hawks might choose and a point the Doves might choose. d. Imagine that an aggressive neighbouring country reduces the size of its military. As a result, both the Hawks and the Doves reduce their desired production of guns by the same amount. Which party would get the bigger "peace dividend," measured by the increase in butter production? Explain.



Answers

Some economists believe that the U.S. economy as a whole can be modeled with the following production function, called the $\textit{Cobb$-$Douglas production function}$: $$Y=AK^{1/3}L^{2/3},$$ where $Y$ is the amount of output, $K$ is the amount of capital, $L$ is the amount of labor, and $A$ is a parameter that measures the state of technology. For this production function, the marginal product of labor is $$MPL=(2/3) A(K/L)^{1/3}.$$ Suppose that the price of output $P$ is 2, $A$ is 3, $K$ is 1,000,000, and $L$ is 1,000. The labor market is competitive, so labor is paid the value of its marginal product.

a. Calculate the amount of output produced $Y$ and the dollar value of output $PY$.
b. Calculate the wage $W$ and the real wage $W/P$. (Note: The wage is labor compensation measured in dollars, whereas the real wage is labor compensation measured in units of output.)
c. Calculate the labor share (the fraction of the value of output that is paid to labor), which is $(WL)/(PY)$.
d. Calculate what happens to output $Y$, the wage $W$, the real wage $W/P$, and the labor share $(WL)/(PY)$ in each of the following scenarios:
i. Inflation increases $P$ from 2 to 3.
ii. Technological progress increases $A$ from 3 to 9.
iii. Capital accumulation increases $K$ from 1,000,000 to 8,000,000.
iv. A plague decreases $L$ from 1,000 to 125.
e. Despite many changes in the U.S. economy over time, the labor share has been relatively stable. Is this observation consistent with the Cobb$-$Douglas production function? Explain.

A racial question, too. Imagine a society that produced is military goods and consumer goods. So we'LL call them guns in butter and we have to drill a production cars possibility frontier for guns and brought her in Explain a shave and on demonstrators. Which point is tio not impression, at which point it's impossible. Also, those are questions A and B. Okay, so then I will draw her Graff with the ex anxious being water and, uh, why exist being guns till there's a trade off between producing these two goods. So the more guns we want, the fewer parts we can produce a same day our way around. So the production frontier is like something like this, and we typically trolled this Randhir is a bow shaped like a concave curve because we assumed that okay, in order to Oh, because he said a state nous here. So he ordered to produce one unit of butter. You have to give up this amount of guns in a a cz we one more in your butter A as we want to produce more and more butter extra. One unit off butter, which is the horizontal one here, forces us to give up on more guns. So but here This is steeper here because the more butter be produced. More guns we have Tio let go off. Okay, so which points are impossible? So as we look at this front here we have You know that I have just erase this. We have to know that everything outside the frontier are impossible because we don't have enough human resource or either for capital to produce this these things, these combination ofthe goods. But all that isthe with Linda. The boundaries for sorry are feasible, but which are the most efficient production combinations. These things on the frontier are the most efficient, most efficient beings that we are extract every possible resource we obtain, and we can have Amanda turned them into look which we want. And so the plank wine is the most efficient. A combination. Okay, So see, imagined that the society has two parties called the hogs and the dopes hawks one want guns and jobs once butter. So which point? Well, they Joe's So apparently the hawks, they want guns race, so they will, like, do whatever they can to produce us more guns as possible. So they don't hear about butter so their bodies can be zero. And for jobs that now let's use our blue A stoves. Ah, boo for dogs. So they want us many butter as possible and they don't care about, so they will choose thiss point. Okay, so so supposed that their aggressive neighbor reduce the size of military. So as a result, they will both hawks and doves will reduce their desired production ofthe guns. But we can. We want to know that which off the two groups get the bigger peace dividend, which is measured by the increase in barter production. So I was oversold firsthand, wised up a case of the horse so they now know that way they don't have to produce that many guns. So they decrease their gun production and they increased their border. They have better production. So the new frontier for the Hawks is like something like Nick's and then on what happened to the dogs because they care less about military comparing to the hawks. So their demand for the gun will decrease even more because they think that Oh, now the world is actually very peace. So what we have tio produce so many guns. So then they decrease a lot. Oh, gone production. So they say these extra resources to produce more butter. So on their butter We're sorry. Sorry decides, you know, God, it's just like something also contain Put it close down here. So at the end, they can produce a more butter than the Hawk group, so they are enjoying more the so called peace dividend.

So in this question, their three people layering mall and curly I will write their names here and they all can provide two kinds of services Oneness. Loewy longs me right through on here laws and the other one days on the washing cars. So cars and here they all have cars. They all have ten units of time. So within an hour, what Larry can do is either no one say one piece of long or one washed one card. Remember, these are our or so within an hour, he can only choose. Either do this or leader to this. Okay, So Mark and either one law or wash two cars and curly can deter a mo Tu Long's or washed one cars. So now we have to compare the following situations. So a situation. They all three people spend all their time mowing lawns. So if they spend all their time doing this on the left hand side, remember they had ten hours, right? So Larry can mo can longs And the moment also ten and curry came all twenty six. So total if I sum this up, forty longs that all three off them tamaang within ten tain ours and situation being if they all spend their time on washing cars. So there's this tape twenty I can attempt to attend here. So some them up. It's also forty. Okay, so this is situation, eh? This is the situation being okay? So now situation see is saying that if off them spend half of their time of each activity so they used bring cover here So half of their time is like five hours. So there has been five hours on the Longs. So he came home five longs and then also washed five cars. And for no, he can't well, five months and he washed tame cars because he speed off washing cars. It's faster. And for for curly, it's the other way around. So he wash Hey, Walt, hand longs and wash five cars because using five hours to wash the car and five powers to alone along. So in total, it's like twenty. And here is also twenty. So if each of them spend half their time doing these two jobs at the end, twenty animals were being alone and twenty cars will be washed. Okay, so this is situation, See? Okay, so let's look at the situation. Think I'll use a car back black. So if I'm Larry spent half his time each activity and no only washes cars and curry only most. The law. So Larry is the same situation seeing he spent have office. I'm doing both And the now mo on ly wash the car so he only do what he is better doing because he wash his car faster. So then he can wash twenty five cars and a CE for curly. He doesn't have to spend time on washing cars. He just concentrate on more longing. Long soap is twenty. So it was something obvious. Five plus twenty. So situation t at the end, twenty five laws will be more and also five plus twenty here. Twenty five cars will be washed. Okay, so we can answer the next question be of graft, the production prop possibilities frontier. I'm for this economy and use your answer in part Aid to identify point a PCD. Okay, so this is home. I don't want to jump to the next page. So I was just I'm drawing here, so to draw Ah, production possibility Frontier, you have to first put these two services on the ex. Ask six and the Y axis. So this long and on the Y axis out ofthe people in this car. So we know that in paying a situation a for Lee logs will be washed and the zero copper will be a mod and zero cars will be washed. So it's like forty and zero so forty like for that long. So this point isthe situation, eh? I will say that the number here is forty and poor situated. Forty cars will be washed and on Nero Long will be more so. Point B is right here and it is also forty. And for situation, see used color green. It's like twenty longs and twenty cars. So it's like the midpoint between these two. So C is here. This is like a I was just not right now the number Okay, I just very die. This is twenty and then also the white axes is ah labeled twenty here. And what about the black ones? So black One is like twenty five hundred twenty five cars. So appointees like to the operate off off point c. So the because it's like twenty five hired in twenty and also twenty, five hundred and twenty So we can see that the production possibility Frontier I'LL go use Frick Color red will be like something like this. I can see that this is not a straight line because the street I should cross this point. See here a street my ship in a c b. But now this front here is like a little bit curved because of this pointy out there. Okay, so once we drew this, well, you answered a fall in question. Um, question c explain why the production possibilities from tear has the ship. It does so Oh, yeah, I just explained that. So we've seen the between the frontier. These are all like production sets that isthe attainable. So within these three three people and human resource, we can produce all these possible combination off products. But what is outside directing? Here we have market like all the thing here are infeasible because we don't have enough young power to our complete the services. Eso es bcd Which one is king official so apparently see is inefficient because things it can attend point deed point the nation, like better allocate their jobs to arm produce them. Most possible the services for each off these two goods so see is inefficient

Pen. Suppose firms become very optimistic about future business conditions and invest heavily in new capital equipment. Question A is asking us to draw on that Grady Man in white diagram to show the short on the facts of this optimism on the honey label. New levels. Prices in real output explain wide every recording about out with supply changes. So this is actually very intuitive because we know now that the firm is going to invest more in capital, say they're going to build new machines or they're going thio buy a new computer that runs faster. So that is why they can produce more output. So the aggregate supply curve is positive, sloping an aggregated menace down we're still being, so we know that things every firm is going to produce more outputs. The supply moves to the right hand side of soup. Quite. Why move to the right hand side? Because there is, like a year Imus increase in the amount. So this is God aggregate supply by prying. All right, So question P Issing that now use the same diagram. They show the long run equilibrium and explain why the aggregate quantity off out with demanded also changes. So first of all, we know that the equilibrium is the blood black dot Over here. So, people, um so the economy is in need off this amount off output sake, You big capital Q and A price level is P. And after the firm decided thio investing capital, they can produce more. So then you look over Miss Watcher, then the old quantity. Why have the price level goes down? Because if the demand why doesn't change, they produce more goods, so they only economy each good has a lower unit price. But this is the first stage of change. What about the second stage? So things we know that the firm are supplying loves off system, for example is an iPhone. I'll be on the market. All those people who work in the firm are earning more profits, Right? So if those workers Wayne go shopping or, uh, do some investment or consumption things near Reacher, they are going to increase the aggregating man as well. Baby man in the one Ron is going to shoot to the right. So this is a the prime. So we now know that the new equilibrium is the ring dot here so they could live removes from black to blue in the short on and in the long run the agreement. It's also going to adjust to increase to catch up with this, like an advancement of technology and capital. So we have this new war, Michael drink at the green dot So then we cannot answer questions. See how my investment boom. We're just the first shift of this blue area over here affect the longer aggregate supply curve. So we know from this chapter that the long ground aggregate supply curve is always vertical, so sinks We know that the original equilibrium is the black dot This wording call why? Which just long run. Um, aggregate supply is going through this black not and us is what I just said. With this transition face the economy ISS eventually going to land at this green dot is the new equilibrium and the aggregate that long on aggregate supply curve is also going to shift to the right. So then we know that in the long run, this investment boom is actually going to help the economy because, um, let's extend this black X axis. Why is it good for the economy. Because at the end, we have this amount off outward, which is sake. You star way larger than the original quantity here. So this is the whole concept off analyzing this question.

Okay, guys, this is chapter 15 Problem. Nine were given this demand equation, total cost equation, marginal revenue and marginal cost equations. And we're told that international trade, at least to begin with, is prohibited. The first part of the question asks us What price? The monopoly company in Witten, um, charges for soccer balls. What quantity will they sell and how much profit the company makes? They are, as always, profit maximizing company's sets its price such that marginal cost equals marginal revenue. And so we have a marginal cost and marginal revenue equations here, so we're going to set them equal to each other. 10 minus two q equals one plus Q until nine equals three Q and three equals the quantity began. Plug this into the demand equation, which is 10 minus. Q equals P 10 minus three equals p, and so price is equal to seven. And we see that the revenue, which equals quantity times price equals three times seven equals 21. And so then we just need to determine pull up as we need to know what the cost is. And here we have, the total cost equals three plus Q plus 30.5 Q Squared, which equals three plus three plus 30.5 times three squared equal six plus half of nine, which is 4.5, equals 10.5. So profits equals 21 minus 10.5, which equals 10.5. The second part of the question asked us if we can, um, now opens up to trade at a world price of $6 and remember that our calculated domestic price is $7. What happens to domestic consumption? We'll have a domestic consumption or production. And what will Wickman become? An importer or exporter of soccer balls? Um, and so it says in the text book. Remember that if the domestic price is lower than the world price than the country become an exporter, and if the price the domestic price is higher than the world price actually, let's say is higher than the world price. Then the country will be an importer. And so, since the domestic price is $7 in the world, price was $6. What name is going to become an importer of soccer balls? So what happens to domestic production? Domestic production is going to decrease, and this is because the company is facing a lower price, and it's also facing an upward sloping, marginal cost curve. And if it can charge, if it can't charge as much, then it's going to have to produce less. Um, domestic consumption, however, is going to increase. And this is because the price of a soccer ball has decreased and they're facing a downward sloping demand curve, which means to lower the price. The more soccer balls they're going to demand in part d. This is asking us. Sorry, I skipped part C. Parsi is asking us if this analysis agrees with our analysis of international trade from chapter nine. I'm gonna let you review chapter nine. But the short answer is that yes, it does. Um, part D of this question is then asking us if the world price were exactly as we calculated in part a of the world price was $7 instead of $6. Would anything have changed in the weakening economy after it was opened up trade? And the answer is still yes, because the producer of soccer balls, uh, now has to be in a competitive market instead of a monopoly market. And this means that the company can no longer charge above. It's marginal revenue. And so when setting marginal cost equals marginal revenue to decide how much to produce, the company now has to set marginal cost equal to demand, to determine how much to produce. So this was Chapter 15 problem nine.


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