Note: Questions 3 and 4 Are Printed on the Other Side of This Sheet

Economics 100B

Spring 2018

Homework #2

Gallet

Note: Questions 3 and 4 are printed on the other side of this sheet.

[1]

A.If the prices of all products are rising at 5 percent per year and your employer gives you a 5 percent salary increase, are you better off, worse off, or equally well off in comparison with your situation a year ago? Use indifference curve analysis to explain your answer.

B.Instead, if the prices of all products are rising at 5 percent per year and your employer gives you a 10 percent salary increase, are you better off, worse off, or equally well off in comparison with your salary a year ago? Use indifference curve analysis to explain your answer.

[2]Ringo enjoys consuming left-handed drum sticks (let Y represent the quantity of left-handed drum sticks consumed) and right-handed drum sticks (let X represent the quantity of right-handed drum sticks consumed). Note that left-handed and right-handed drum sticks are most often used together (i.e., they are consumed “hand-in-hand”). To account for this, suppose Ringo’s total utility (denoted U) is represented by the following “utility function”:

U = 100∙min(X,Y)

How do we interpret this function? U is simply 100 times the minimum of X and Y. For example, if Ringo consumes 5 left-handed drum sticks (i.e., Y = 5) and 2 right-handed drum sticks (i.e., X = 2), then min(X,Y) is the smaller of X and Y, or 2. Thus, U = 100∙2 = 200 utils. Instead, if Y = 5 and X = 8, then min(X,Y) = 5, making U = 100∙5 = 500 utils. If X = Y = 5, then min(X,Y) = 5, making U = 100∙5 = 500 utils.

A.With Y on the vertical axis and X on the horizontal axis, sketch Ringo’s indifference curve corresponding to U = 500.

B.Holding Y constant at 5, explain why Ringo’s consumption of X does not adhere to the law of diminishing marginal utility.

C.Given Ringo’s income is $100, the price of X is $1, and the price of Y is$1, illustrate his budget line, being careful to provide the vertical-axis and horizontal-axis intercepts.

D.Continuing part C, what is Ringo’s (total) utility maximizing bundle of X and Y, given his budget constraint? What is his total utility at this bundle? Provide an illustration of your answer.

E.Suppose George recommends the governmentimposean excise tax on the consumption of right-handed drum sticks. Denoting income as I, the price of X and PX, the price of Y as PY, and the excise tax as t, what is the equation for Ringo’s budget constraint? With I = $100, PX = $1, PY = $1, suppose the tax rate t is set at $0.25. Compared to your answer in part C, illustrate how the imposition of this tax affects Ringo’s budget line, being careful to provide vertical-axis and horizontal-axis intercepts. Given this new budget line, what is Ringo’s (total) utility maximizing bundle of X and Y? What is his total utility at this bundle? Provide an illustration of your answer.

F.Continuing part E, nowPaul wantsthe government toprovide Ringo an income subsidy (i.e., raise his income) in order to offset the negative impact of the excise tax of $0.25 on Ringo’s total utility. That is, he proposesthe government provide compensation to Ringo sufficient to return his total utility to its level in part D. Note that this is identical to compensating variation (CV). As such, what is the value of CV under this proposal?

G.John provides an alternative recommendation to return Ringo’s total utility to its level in part D. Specifically, with I = $100, PX = $1, PY = $1, t = $0.25, he recommendsthe government give Ringo a per unit subsidy (labeled s) for every left-handed drum stick he consumes. What is the value of s sufficient to restore Ringo’s total utility back to its level in part D?

H.Having final say on which policy is best at restoring Ringo’s total utility, Brian considers John and Paul’s proposals, and is charged with selecting that proposal which is economically efficient (i.e., cost the government the least amount of money). Which policy does Brian prefer, or is he perhaps indifferent between the two?

[3]Track 8, a local microbrewery, hires an economist to analyze its short run production. However, the economist samples too much of the company’s product, and is fired in the process. Unfortunately, much of the production data is missing, as evidenced in the table below. Believing that college students never consume alcoholic beverages, the company decides to hire you to complete the missing portions of the table.

1. Complete the missing portions of the production table below.

B.Even an inebriated economist knows, from the standpoint of profit maximization, the brewery should never hire 5 workers. Carefully explain why utilizing the concept of efficiency.

[4]A firm uses workers (labor) and robots (capital) to produce a particular product. As the production manager for this firm, you know the firm’s production function is given by the following equation: Q = 2K + L, where Q is quantity of the product produced, K is the number of robots used, and L is the number of workers hired.

A.Carefully graph the isoquant corresponding to 50 units of output.

B.Carefully explain whether this firm encounters increasing, constant, or decreasing returns to scale.

C.If the price of labor is $20 and the price of capital is $30, what values of K and L should you employ in order to produce 50 units of output in an economically efficient way? Illustrate your answer by graphing an appropriate isoquant and isocost line. What is the firm’s total outlay at this combination of K and L?

D.If the price of labor decreased to $10, while the price of capital increased to $40, what values of K and L should you now employ to produce 50 units of output in an economically efficient way? Illustrate your answer by graphing an appropriate isoquant and isocost line. What is the firm’s total outlay at this combination of K and L?