Economics 100B - California State University, Sacramento



Economics 100B

Spring 2020

Homework #2

Gallet

Note: Question 4 and 5 are printed on the other side of this sheet.

[1]

A. Suppose Amrit is a student at Sacramento State. His parents give him $1200 each semester to buy textbooks for his courses from the university bookstore. Currently, at the bookstore the price of a new textbook is $200 and the price of used textbook is $50. With the quantity of used books on the vertical axis and the quantity of new books on the horizontal axis, illustrate Amrit’s budget line, being carefully to indicate the horizontal and vertical axis intercepts, as well as the slope.

B. Suppose the bookstore raises the price of new textbooks 20% and also raises the price of used textbooks 60%. Assuming Amrit’s parents continue to give him $1200 to buy textbooks, illustrate the impact of this on Amrit’s budget line (being careful to indicate the horizontal and vertical axis intercepts and slope).

C. Now, at these higher textbook prices, suppose that Amrit’s parents decide to double the amount they give him to buy textbooks. Using an appropriate graph, and assuming Amrit wishes to maximize his utility (subject to his budget constraint) will he be better off, worse off, or you simply do not know (given the information), compared to part A above?

D. Suppose the bookstore at Sacramento State lowers its prices back to those given in part A, causing Amrit’s parents to return their textbook funding to $1200. Now consider Brenda, who is a student at UC Davis. Her parents also give her money to buy new and used textbooks at the UC Davis bookstore. The price of a new textbook at UC Davis is $200 and the price of a used textbook is $100. Assuming both Amrit and Brenda want to maximize their respective utilities, will Amrit and Brenda have the same marginal rate of substitution between used and new textbooks? If not, which one will have a higher marginal rate of substitution (in absolute value)?

[2] Amedeo consumes tacos and burritos. Suppose his marginal utility for tacos and his marginal utility for burritos are constant at 4 (i.e., irrespective for how much he consumes of each good, marginal utility of each good equals 4). Also, the price of a taco equals $1, the price of a burrito equals $2, and Amedeo’s income (budget) equals $20.

A. Using a graph, illustrate Amedeo’s utility-maximizing bundle of tacos and burritos, being careful to illustrate his budget line and indifference curve.

B. Now, suppose the price of a taco increases to $3. Using a graph, illustrate how this influences Amedeo’s optimal bundle of tacos and burritos.

[3]

A. You are the manager of a firm which sells its output at a price of $40 per unit. You are interested in hiring a new worker who you expect will increase your firm’s output by 2,000 units per year. What is the most you should be willing to pay this worker per year to come to your firm?

B. Suppose a firm currently pays all of its production workers a wage equivalent to the average revenue product of the firm (which equals the price of the firm’s output times the firm’s average product). Compared to the average, imagine worker 1 is very productive, while worker 2 is not very productive. Carefully explain why worker 1 would prefer to be paid a wage equivalent to their marginal revenue product, while worker 2 is content being paid a wage equivalent to average revenue product.

[4] Beer-R-Us, 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.

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

|Quantity of Labor |Quantity of |Marginal Product of Labor |Average Product of Labor |Total Product of Labor |

| |Capital | | | |

|0 |10 |--- |--- | |

|1 |10 |1000 | | |

|2 |10 | |1250 | |

|3 |10 | | |4500 |

|4 |10 | |1500 | |

|5 |10 |-1500 | | |

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

[5] Suppose a firm employs capital (K) and labor (L) to produce a product with the following production function: Q = min(K, L), where Q is the quantity produced and min(K, L) is the minimum (i.e., smallest) value of K or L. For example, if K = 20 and L = 30, then Q = 20 (since the smallest value of K or L at this combination is 20); if K = 30 and L = 20, then Q = 20 (since the smallest value of K or L at this combination is 20); if K = L = 20, then Q = 20 (since both K and L have the same value, making the smallest value 20 at this combination).

A. Graph the isoquant corresponding to Q = 20.

B. Suppose the price of capital (PK) = 5 and the price of labor (PL) is 1. Determine the best combination of K and L to produce 20 units of output, if the goal of the firm is to minimize the expenditure to produce this quantity. Illustrate a graph (depicting the isoquant and isocost) consistent with this choice of K and L. What is the firm’s total outlay (i.e., total cost) at this combination?

C. Suppose the price of capital increases to 10, while the price of labor remains at 1. Determine the best combination of K and L to continue to produce 20 units of output, if the goal of the firm is to minimize the expenditure to produce this quantity.

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