Problem Set #3Suggested Solution(a) Marginal Revenue Product -The change in revenue as a result of a change in production input such as labor.(b) Iso -Cost Curve 一A curve illustrating all input combinations that can be purchased for a given total cost, TC.(c) Cost-Minimizing Input Choice 一The least expensive input combination that yields a certain desired output level Q.(d) Marginal Cost -The change in total cost as a result of a small increase in units produced.2.(a) Large Substitution effect - for a given change in relative price, the change in the optimal consumption bundle is large.The substitution effect will be larger as the indifference curve is flatter. A relatively flat indifference curve represents a consumer who views the two goods we consider as good substitutes and therefore is more responsive to a given change in relative price.The extreme case is a straight line indifference curve representing perfect substitutes. In such a case, as the relative price change the consumer can move from one extreme case of purchasing only one good to purchasing only the other good (corner solutions). A relatively flat indifference curve will occur when the two goods wc consider arc similar.(b) Large Income effect 一 as the purchasing power change, the change in the optimal consumption bundle is large.A large income effect will happen when the percentage spending on the good we consider, out of our total income, is large. Related to this, income effect for a luxury good is large relatively to the income effect for a necessity.(c) Demand more Elastic 一Recall that the relationship between price and quantity demanded is a result of both the substitution and income effect, i.e. the total effect. As the total effect is greater, the responsiveness to a change in price is greater, meaning a flatter and more elastic demand curve.Assuming a downwards sloping demand curve, the larger the substitution effect the larger is the total effect, leading to a flatter and more elastic demand curve. A large substitution effect is a result of a relatively flat indifference curve, as explained in (a). In addition, because the total effect is composed also from the income effect, then a large normal income effect, will lead to a more elastic demand curve. A large income effect is a result of the factors mentioned in (b). Notice that an income effect for an inferior good is in the opposite direction to the substitution effect and thus decreases the total effect generating a less elastic demand curve, all else equal.(d) Upwards sloping demand curve - the relationship between price and quantity demanded is a result of both the substitution and income effect, i.c. the total effect. Substitution effect is always in the direction of a downwards sloping demand curve. Thus, to have an upwards sloping demand curve, we need to have an income effect that is stronger than, and in the opposite direction of, the substitution effect. An income effect,in the opposite direction of substitution effect, is the case of inferior good. Therefore, if we have an inferior good, where the income effect dominates the substitution effect then theoretically we will have an upwards sloping demand curve. Such a good is a special case and is called a Giffen good.(e) Complements in Demand - Consider two goods x and y. These two arePx J 0 Jcomplements in demand if, for example, ,、.EqSuppose P、T: substitution effect leads to buying more of good y and purchasing power decreases. We are given that the total effect of Px T on consumption of y is negative (purchasing less of y). This implies that as purchasing power decreases we buy less of y. Moreover, the income effect needs to be stronger than the substitution effect to receive a final decrease in the quantity of y. The conclusion is that y must be a normal good (purchasing power decreases 一 we decrease the amount of y) and to have a small substitution effect (such that the income effect will dominate.)One can do the same exercise for a change in P、and will get similar conclusions regarding good x.To summarize, for complements in demand, the two goods need to be normal and to have a small substitution effect.3.(a)In the graph below we illustrate the Marginal Productivity of labor (MP) and Marginal Revenue Product of Labor (MRPt ). These two are downwards sloping curves, since they reflect diminishing marginal productivity of labor - as wc have more workers, the marginal productivity of an additional worker declines. You can see that also by analyzing the fonnula: MPt =- . As more workers are employed, L increases (in the2Ldenominator) and MP、decreases.An equivalent way to see this is:、2K.equation: P x 厂=W and is equal toL =The optimal labor in the short run is determined by: MRPL = W .MRPl is defined as Px MPL = Px . Thus, L is determined by the following 2 J LP_2W )(c)mpl, mrpl, wWageIncreaseWageDecreaseIncrease in LaborDecrease