General Equilibrium 203

Transcription

1 General Equilibrium. Peanut butter has always been thought to be a delicious, wholesome food. That is, until the FD releases its Food Defect Guidelines that set maximum allowable amounts of rodent excreta that may be present in every jar (surprisingly, the maximum is not zero!). Following this release, the demand for peanut butter falls. a. What is the immediate effect on the price of peanut butter and the quantity consumed? b. Peanut butter and jelly are complements. What is the residual effect on the price of jelly? c. What effect does the change in the price of jelly you indicated in part (b) have on the demand for peanut butter? d. Does the demand effect you indicated in part (c) tend to push peanut butter prices and quantities back toward their original values, or farther away from them?. a. The price of peanut butter decreases and so does the quantity consumed. b. The demand for jelly decreases as a result of the decrease in the price of peanut butter; hence, the price of jelly decreases. c. s the price of jelly decreases, the demand for peanut butter increases. d. In the first stage, the demand decreased. In the second stage, as a result of a decrease in the price of jelly, the demand increased. Thus, the demand effect indicated in part (c) tends to push peanut butter prices and quantities back toward their original values. *. Following a renewable fuels mandate in, the demand for yellow corn, the key ingredient in ethanol, skyrocketed. a. What is the immediate effect of the increase in demand on the price and quantity of yellow corn? b. Yellow corn and white corn (the key ingredients in corn tortillas) are substitutes in production. s a result of the changes in the market for yellow corn, what happens to the supply of white corn? c. How does the changing supply of white corn affect its market price? d. s the price of white corn changes, what effect does that change have on the supply of yellow corn? Indicate the likely effects on both the price and quantity of yellow corn produced. e. Does the change in the price of white corn tend to push yellow corn prices and quantities back toward their initial values, or farther away from them?. a. The price and quantity of yellow corn increase. b. The supply of white corn decreases because farmers shift some of their production from white corn to yellow corn. c. The market price of white corn increases. d. s a result of the increase in the price of white corn, the supply of yellow corn decreases as the farmers now shift some of their production back toward white corn. The price of yellow corn increases and the quantity decreases. e. The increase in the price of white corn tends to push yellow corn prices further away from its initial value (as both shift, the increase in demand and the decrease in the supply of yellow corn push prices upward, whereas the quantity is pushed back toward its initial value). *. The following statements describe supply and demand conditions in the markets for cheese and wine, respectively. The demand for cheese is given by Q d c = P c P w, where Q d c is the quantity of cheese demanded each week in ounces, P c is the price of a pound of cheese, and P w is the price of a bottle of wine. The demand for wine is given by Q d w = P c P w. The supply of cheese is given by Q s c = P c. The supply of wine is given by Q s w = P w. a. re wine and cheese linked on the supply side of the market, or on the demand side? b. Equate supply and demand in the cheese market, and simplify to express the price of cheese as a function of the price of wine. c. Equate supply and demand in the wine market, and simplify to express the price of wine as a function of the price of cheese. d. Substitute the expression for the price of wine you found in (c) into the equation you found in (b) to solve for the price of cheese.

2 Part Beyond the Basics e. Plug the price you calculated in (d) into the expression you derived in (c) to solve for the price of wine. f. Plug the prices of wine and cheese you found in (d) and (e) back into either the supply or demand functions for wine and cheese to find the equilibrium quantities of wine and cheese that will be sold.. a. Wine and cheese are linked on the demand side of the market. b. Q d s c = P c P w = P c = Q c P c =. P w c. Q d s w = P c P w = P w = Q w P w =. P c d. P c =. P w =.(. P c ) = P c.7 P c = 7. P c = $ e. P w =. P c =. = $ f. Q w = P c P w = = Q c = P c P w = =. Consider the wine and cheese problem you solved in Problem. Suppose the demand for wine changes so that at every price, fewer bottles are demanded. a. Hold the price of cheese constant, and calculate the partial equilibrium effects of the change in the demand for wine. What happens to the price? What happens to the quantity? b. Plug the new price of wine into the demand for cheese. Does the shock to the wine market cause the demand for cheese to increase or decrease? c. Calculate the effect of the change in demand for cheese on the price of cheese and the quantity of cheese sold. d. Plug the new price of cheese into the demand for wine. Does it cause the demand for wine to increase or decrease? Does the wine market get pushed farther from its initial equilibrium, or back toward it? How will these changes in the wine market feed back into the cheese market? e. Following the steps taken in Problem, but using the new cheese demand function, solve for the new general equilibrium price and quantity of both wine and cheese. f. How does the final general equilibrium price and quantity of wine you calculated in (e) compare to the partial equilibrium effects you calculated in part (a)?. a. Equating the new demand for wine and supply for wine, we get Q d s w = P c P w = P w = Q w P w =. P c Holding the price of cheese constant at $, the price of wine falls from $ to $. Similarly, the quantity of wine sold falls from bottles to. b. Originally, the demand for cheese was given as Q d c = P c P w. With wine priced at $, we can substitute to find cheese demand given as Q d c = P c. When the price of wine falls to $, cheese demand changes to Q d c = P c. The shock to the wine market causes the demand for cheese to increase. c. Equating supply and demand in the cheese market, Q d c = P c = P c = Q s c. Solving, P c = $., and plugging that price into the supply curve, Q c =. units. Therefore, the price of cheese increases by $. and the quantity sold increases by.. d. P w =. P c = $.7 = Q w The demand for wine decreases as a result of higher cheese prices. Both price and quantity fall (to $.7 and.7 units, respectively) as a result. The wine market gets pushed farther from its initial equilibrium. In the case of the cheese market, the decrease in the price of wine will cause the demand for cheese to increase. e. The price for cheese is Q d s c = P c P w = P c = Q c P c =. P w The price for wine is Q d s w = P c P w = P w = Q w P w =. P c

3 General Equilibrium Chapter To find the equilibrium prices of wine and cheese, we calculate P c =.P w =.(.P c ) = +.P c.7 P c = P c = $. The equilibrium quantities are P w =. P c =.. = $. Q w = P c P w =. Q c = P c P w =. f. The price and quantity of wine decrease by more than. In the final equilibrium outcome, both price and quantity decline by... Suppose that lettuce and tomatoes are goods that are related on the demand side of the market, and that both markets are in equilibrium. George and Janet are analyzing the effect of an increase in the demand for tomatoes. George is using a partial equilibrium framework, and Janet is using a general equilibrium framework. a. True or False: George will predict a larger increase in the price of tomatoes than Janet will. Explain. b. True or False: George will predict a larger increase in the quantity of tomatoes sold than Janet will. Explain. c. True or False: The answers to parts (a) and (b) depend on whether lettuce and tomatoes are complements or substitutes. Explain.. a. If one assumes tomatoes and lettuces are complements, the statement is false. If the demand for tomatoes increases, causing tomato prices to rise, the demand for lettuce will decrease as a consequence. The fall in the price of lettuce will cause a further increase in the demand for tomatoes, driving prices even higher. Janet s analysis will pick up that second increase; George s won t. b. The statement is false. Given that the demand for tomatoes will increase twice, as we saw in part (a), Janet s analysis will again pick up the secondary effects and predict a larger increase in the quantity of tomatoes sold. c. The statement is false. Consider what happens if tomatoes and lettuce are substitutes. The initial increase in the demand for tomatoes causes the price to increase. s a result, the demand for lettuce increases, driving up its price. But, the increased price of lettuce feeds back into the tomato market, causing demand to further increase. Thus, at least qualitatively, the effects do not depend on the nature of the relationship (substitutes or complements) between lettuce and tomatoes.. In the central United States, farm ground is devoted to corn and beans as far as the eye can see. The supply of beans (in millions of bushels) is given by Q s b = P b P c. The supply of corn is given by Q s c = P c P b. Let the demand for beans be given by Q d b = P b, and the demand for corn be given by Q d c = P c. a. Solve the general equilibrium price and quantity of both beans and corn. (Hint: If you have trouble with this step, follow the procedures outlined in Problem.) b. Suppose there is a shock to bean demand so that the quantity demanded at each price increases by 8 million bushels. The new demand for beans can be written as Q d b = 8 P b. Solve for the new general equilibrium price and quantity of beans and corn. c. What happens to the price of beans and the quantity sold as a result of the demand increase? d. What happens to the price of corn and quantity sold as a result of the increase in the demand for beans? Explain.. a. Equating the supply and demand for beans, we get Q s d b = P b P c = P b = Q b P b = + _ P c Similarly for corn, we obtain Q c s = P c P b = P c = Q c d P c = + _ P b

4 Part Beyond the Basics Solving for the general equilibrium prices, we get P b = + _ P c = + _ ( + _ P b ) =. + _ 9 P b = $ P c = + _ P b = + _ = $ The equilibrium quantities are Q b = P b P c = P b = Q c = P c P b = P c = b. Equating the supply and demand for beans, we get Q s d b = P b P c = 8 P b = Q b P b =.7 + _ P c Similarly for corn, we obtain Q s d c = P c P b = P c = Q c P c = + _ P b Solving for the general equilibrium prices yields P b =.7 + _ P c =.7 + _ ( + _ 8_ 9 P b = P b = $8 P c = + _ P b = + _ 8 = $ The equilibrium quantities are Q b = P b P c = = Q c = P c P b = 8 = P b ) = + _ c. The price of beans increases by $ per bushel and the quantity increases by million bushels. d. The price of corn increases by $ per bushel and the quantity decreases by million bushels. Since the demand for beans increased, more land was devoted to bean production and less to corn. The supply of corn decreased, raising its price and reducing its quantity. 9 P b 7. You are a USD pork analyst, charged with keeping up to date on developments in the market for the other white meat. Recently, the demand for beef decreased. a. Explain how pork and beef might be linked on the demand side of the market. b. Explain how pork and beef might be linked on the supply side of the market. c. You notice that within a few months, the overall quantity of pork being sold increases. Is this fact consistent with a demand-side link between beef and pork, or a supply-side link? 7. a. Consumers treat pork and beef as substitutes. Hence, if the price of pork increases, the demand for beef increases and vice versa. b. Producers can rear either pigs or cows. For example, if the price of pork increases, other things being equal, some of the farmers who breed cows will switch to rearing pigs as pigs and cows become substitutes in production. c. This fact is consistent with a supply-side link between beef and pork. When the demand for beef decreases, the price of beef falls. Consequently, the suppliers shift resources toward producing more pork. That leads to an increase in the supply of pork, which results in higher quantities (and lower prices) in the pork market. 8. Bob, Carol, and Ted are residents of a tiny commune in darkest Peru. Bob currently has a utility level ( U b ) of utils, Carol s utility ( U c ) is utils, and Ted s utility ( U t ) is utils. lice, the benevolent ruler of the commune, has discovered a policy that will allow her to redistribute utility between any two people she chooses in a util-to-util transfer. a. If lice believes the social welfare function is given by W = min( U b, U c, U t ), i. Recommend a transfer that will improve social welfare, if any such transfers are possible. ii. What is the highest level of welfare that the commune can achieve, and how must utility be divided among Bob, Carol, and Ted?

5 General Equilibrium Chapter 7 8. a. b. If lice believes the social welfare function is given by W = U b + U c + U t, i. Recommend a transfer that will improve social welfare, if any such transfers are possible. ii. What is the highest level of welfare that the commune can achieve, and how must utility be divided among Bob, Carol, and Ted? c. If lice believes the social welfare function is given by W = U b U c U t, i. Recommend a transfer that will improve social welfare, if any such transfers are possible. ii. What is the highest level of welfare that the commune can achieve, and how must utility be divided among Bob, Carol, and Ted? b. c. i. lice should tell Bob to transfer. utils to Ted. Thus, W = min( U b, U c, U t ) =.. ii. The highest level of welfare that the commune can achieve is ( + + )/ =., so that Bob, Carol, and Ted divide their utils equally among each other. i. The social welfare is regardless of the transfer made. Thus, it is not necessary for lice to impose any transfer. ii. The highest utility that can be achieved is. It does not matter how the utilities are divided. i. Initially, the social welfare is W = U b U c U t = 9,. If lice told Bob to transfer. utils to Ted, the social welfare would be W = U b U c U t =.. =,98.7. ii. The highest level of welfare that the commune can achieve is W max = U b U c U t =... = $7,.9, so that Bob, Carol, and Ted divide their utils equally among each other. 9. l has found $, and has decided to divide it between his children Bud and Kelly. a. If l believes that a fair division means giving equal amounts of cash to everyone, how much should he give to Bud and Kelly? b. Suppose that Bud is rich and Kelly is poor. ssume that the marginal utility provided by a dollar declines the richer you are. If l wishes to ensure that his gift provides the greatest possible collective happiness to his children, how should he divide the cash? c. Suppose that Bud is rich and Kelly is poor. ssume that the marginal utility provided by a dollar declines the richer you are. If l is concerned with distributing equal happiness to Bud and Kelly, how should he divide the cash? d. How do each of your answers to (a), (b), and (c) align with some notion of fairness? 9. a. l should give $ to Bud and $ to Kelly. b. l should give more to Kelly and less to Bud (if any). c. l should give more than $ to Bud and less than $ to Kelly. d. Depending on whom you ask, the prescriptions in either (a), (b), or (c) might be viewed as fair divisions. Each allocation satisfies some notion of fairness.. bel, Baker, and Charlie are identical triplets with identical tastes. The utility they get from consuming various amounts of bacon, eggs, and cheese is summarized in the following table: # of Units Consumed Utility from Bacon Utility from Eggs Utility from Cheese Thus, if bel has pieces of bacon and eggs, his total utility will be 9 +, or. a. Suppose that bel initially has pieces of bacon, Baker has eggs, and Charlie has pieces of cheese. ssuming that bacon, eggs, and cheese all trade one-for-one in the marketplace, suggest a series of Pareto-improving trades that will raise everyone s overall utility.

6 8 Part Beyond the Basics b. What allocation does each end up with when all gains are exhausted? c. Show that once all gains are exhausted, if we force bel to trade any of his goods for any of Baker s goods, neither will be made better off, and at least one will be made worse off.. a. Initially, bel s utility is, Baker s, and Charlie s. If bel exchanges piece of bacon for egg with Baker, and Baker exchanges egg for piece of cheese with Charlie, their utilities are,, and 7, respectively. dditionally, if bel exchanges piece of bacon for piece of cheese with Charlie, and Baker exchanges more egg for piece of cheese with Charlie, their utilities are,, and, respectively. b. The allocations are as follows: pieces of bacon, eggs, and piece of cheese (); piece of bacon, eggs, and pieces of cheese (); pieces of bacon, egg, pieces of cheese (). c. Suppose that bel ends up with pieces of bacon, eggs, and piece of cheese and Baker ends up with pieces of bacon, egg, and pieces of cheese. The table below represents all the possible outcomes from further reallocations: bel pieces of bacon, eggs, piece of cheese piece of bacon, eggs, pieces of cheese piece of bacon, eggs, piece of cheese Baker pieces of bacon, egg, pieces of cheese pieces of bacon, egg, piece of cheese pieces of bacon, pieces of cheese Utilities (bel, Baker) (, ) (, ) (, ) If we continue calculating utilities for both bel and Baker, we will see that if they trade, at least one of them will be made worse off. *. Consider the Edgeworth box diagram at the right, which illustrates the number of peaches and pints of cream in the refrigerator of Billy Joe and Bobby Sue. a. How many peaches do Billy Joe and Bobby Sue have in their fridge? b. How much cream do Billy Joe and Bobby Sue have in their fridge? c. Suppose that Billy Joe pulls peaches and pint of cream out of the fridge, and says, You can have the rest to Bobby Sue. Illustrate this allocation of peaches and cream by placing a point in the Edgeworth box. Label the point. d. Bobby Sue pulls the remaining peaches and cream out of the refrigerator, and comments, Hey I m a bit long on cream and short on peaches here. Give me a couple of your peaches and take one of my creams. Represent this reallocation of peaches and cream by placing a second point in the Edgeworth box. Label the point B. e. Billy Joe happens to find a couple of extra peaches behind last night s gnocchi leftovers, and proudly proclaims, Finders keepers! Represent the effects of Billy Joe s discovery by altering your Edgeworth box. ssume that Bobby Sue acknowledges and respects the finders, keepers rule. Billy Joe s cream Bobby Sue s peaches Billy Joe s peaches Bobby Sue s cream

7 General Equilibrium Chapter 9. a. They have peaches in their fridge. b. They have pints of cream in their fridge. c. and d. Bobby Sue s peaches Billy Joe s cream B Billy Joe s peaches e. Suppose Billy Joe happens to find extra peaches and is permitted to keep them. Bobby Sue s cream Billy Joe s cream Bobby Sue s peaches Billy Joe s peaches B Bobby Sue s cream. Consider the Edgeworth box below, which represents the amount of tea and crumpets available to Eliza and Henry. Henry s crumpets Eliza s tea 7 Eliza s crumpets 7 a. Suppose that Eliza and Henry are currently at point. How many servings of tea and how many crumpets are each enjoying? b. Suppose that while Eliza is using the powder room, Henry takes cups of tea from Eliza. Feeling guilty, he leaves of his crumpets on her nightstand before hastily making his exit. Show that this reallocation of tea and crumpets is a Pareto improvement. c. Show that if Henry had left only crumpet on Eliza s nightstand, the reallocation would not have represented a Pareto improvement. U H U E Henry s tea

8 Part Beyond the Basics. a. Eliza is enjoying servings of tea and crumpets. Henry is enjoying serving of tea and crumpets. b. Henry is better off moving to a higher utility curve, whereas Eliza is not worse off staying on the same utility curve U E. This confirms that such a reallocation is Pareto-improving. Henry s crumpets 7 c. Eliza s tea Eliza s tea U H U H U E 7 Eliza s crumpets Henry s crumpets 7 U H U H U E 7 Eliza s crumpets lthough Henry moves to a higher utility curve U H, Eliza would be worse off moving to a lower utility curve U E. This allocation is not Pareto-improving compared to the initial allocation. U E Henry s tea Henry s tea. Johnny and June are divorcing and must divide their music collection, which contains two types of music: country and folk. mediator suggests an initial division of the collection. Given the initial division, Johnny s MRS between folk and country is, and June s MRS is. a. Use an Edgeworth box to show that the allocation of music is inefficient. Be sure to draw indifference curves for both Johnny and June, and to show their respective marginal rates of substitution at the initial allocation. b. Suggest a general reallocation that could potentially make both parties better off. Explain who would have to give up folk music and who would have to give up country. c. fter some reallocation, Johnny s MRS and June s MRS are equal. Show that the allocation is Pareto-efficient.. a. MRS FC = means that Johnny is willing to forgo up to country music collections to obtain additional folk music collection. June would exchange folk and country music on a -to- basis. June s folk Johnny s countr y June MRS FC = - Johnny MRS FC = - Johnny s folk June s countr y

9 General Equilibrium Chapter b. The reallocation should be made such that MRS Johnny FC = MRS June FC. Since Johnny s MRS is greater than June s, he should exchange some of his country music collection for some of June s folk music collection. c. June s folk U U Jo Jo Johnny s country U Ju U Ju U Ju UJo U Jo June s country Johnny s folk The reallocation is Pareto-efficient as the indifference curves are now tangent; that is, there is no further reallocation that would be Pareto-superior to the one presented above.. Consider the following Edgeworth box diagram that illustrates the preferences of Ed and Peggy for fish and chips: Peggy s fish Ed s chips U E Peggy s chips E P U E U P U P U P U U E U Ed s fish Draw the consumption contract curve corresponding to these preferences. (Hint: You may need to add some indifference curves to the diagram.). Peggy s fish Ed s chips U E U E Peggy s chips U P U E U P U P U U P E Ed s fish *. Chris and Pat like both beer and pizza. Chris views pizza and beer as perfect one-to-one substitutes. Pat believes that beer and pizza are perfect complements, and always consumes them in one-to-one proportions. a. Construct an Edgeworth box for Chris and Pat. b. Derive the contract curve for Chris and Pat. What shape will it take?

10 Part Beyond the Basics. a. and b. Pat s beer Chris s pizza Contract U P curve U P U P U C U P U C U C U C Pat s pizza Chris s beer The contract curve will be at a -degree line.. Bill and Ted like apples and oranges. Bill is always willing to substitute apple for orange. Ted is always willing to substitute apple for oranges. a. ssume that there are apples and oranges to split between Bill and Ted. Construct an appropriately sized Edgeworth box for them. b. Draw indifference curves for both Bill and Ted in your Edgeworth box. Draw Bill s indifference curves with thick lines, and Ted s with thin lines. (Hint: Remember that both Bill and Ted believe that apples and oranges are perfect substitutes!) c. Demonstrate that any initial allocation of apples and oranges in which Bill and Ted each have some apples and some oranges is Pareto-inefficient. d. Find a few Pareto-efficient allocations; then shade the consumption contract curve. (Hint: You showed in part (c) that both parties having both goods couldn t be efficient!). a., b., and d. lthough both Bill and Ted view apples and oranges as perfect substitutes, they do not view them as substitutable in the same proportions. Hence, their marginal rates of substitution are different. Bill s apples Ted s oranges Contract curve U B U B U B Bill s oranges c. Suppose that Bill has oranges and apples and Ted has oranges and apples. If Bill exchanges with Ted any of his apples for oranges, he will be indifferent, whereas Ted will be better off moving to a higher indifference curve. If Bill gives all of his apples to Ted and Ted gives all of his oranges to Bill, they will end up in the Pareto-efficient allocation (the solution in the lower right corner). lternatively, assume that Bill has apples and oranges, while Ted has apples and oranges. There is no potential reallocation that will make either better off without making the other worse off. U T U T U T U T Ted s apples

11 General Equilibrium Chapter * 7. The Edgeworth box on the right shows how castaways Tom and Hank are allocating labor and capital to the production of two goods, food and clothing. The economy is currently at point. a. How many units of labor and capital are being used in the production of each good? b. How many units of food are being produced? Clothing? c. Suggest a simple reallocation of labor and capital between food and clothing that will enable Tom and Hank to enjoy more food and clothing than they currently produce. Capital inputs for food Labor inputs for clothing 8 7 Q F = Q C = 7 8 Labor inputs for food Capital inputs for clothing 7. a. There are labor inputs for food and for clothing. There are capital inputs for food and for clothing. b. units of food and units of clothing are being produced. c. Suppose that one less unit of labor and one additional unit of capital are being used in the food production. Hence, one more unit of labor and one less unit of capital are being used for clothing. This reallocation will enable Tom and Hank to enjoy more food and clothing than they are currently producing. Capital inputs for food Labor inputs for clothing 8 7 Q F = Q C = 7 8 Labor inputs for food Capital inputs for clothing 8. On a small tropical island, two firms draw on the same supply of labor and capital. The first firm produces fish, and in the fishing industry the marginal product of labor is 8 and the marginal product of capital is. The second firm produces coconut, and in the coconut industry the marginal product of labor is and the marginal product of capital is. a. Show that the allocation of labor and capital between the two industries is inefficient. b. Suggest a reallocation of labor and capital that will enable the island to produce more fish and coconuts without using more resources. 8. a. For the allocation to be efficient, the following must hold: MRT FC = MP F _ L MP = MP F _ K C C L MP K or MRT FC = MP F _ L MP = MP C _ L F C K MP K In our case, the allocation is inefficient because MRT FC = MP F _ L MP = _ 8 F K _ = MP C _ L C MP K b. In order for this equality to hold, the left-hand side needs to increase and the right-hand side needs to decrease. This happens when the fishing industry decreases its use of labor (increasing the marginal product of labor in that industry) and increases its utilization of capital (thereby decreasing the marginal product of capital in that industry). The reverse is true for the coconut industry. Therefore, the fishing industry should give some of its labor to the coconut industry in return for some of the capital that is presently utilized in the coconut industry.

12 Part Beyond the Basics * 9. Consider the production contract curve in the graph on the right that illustrates efficient allocations of labor and capital to the production of two goods, guns and roses. a. Use the information in the production contract curve to draw the production possibilities frontier for guns and roses. Put roses on the horizontal axis and guns on the vertical axis. ssume that when all resources are devoted to gun production, guns can be produced; when all resources are devoted to rose production,, roses can be grown. b. Locate point X in the Edgeworth box. Draw a corresponding point X on your production possibilities frontier. Be as accurate as possible in locating this point. Capital inputs for guns Labor inputs for roses Q G = Q G = 9 Q G = Q R = 7 X Q R =, Q R =,8 Labor inputs for guns Capital inputs for roses 9. a. and b. Guns 9 7 X PPF,,8, Roses. Consider the production possibilities frontier depicted below, which shows the different combinations of guns and roses an economy can produce when it uses all its inputs efficiently. Quantity of guns PPF Quantity of roses a. If the MRT at point is., and the marginal product of labor in the gun industry is, what must the marginal product of labor be in the rose industry? b. If the MRT at point is., the marginal product of capital in the gun industry is, what must the marginal product of capital in the rose industry be?. a. b. MRT GR = = MP G _ L R MP L MP R L = MP L The marginal product of labor in the rose industry is. G _ = _ = MRT GR = = MP G _ K R MP K MP R K = MP G _ K = _ = The marginal product of capital in the rose industry is.